Are there any philosophies that share or are similar to my personal philosophy?... Is there an actual duty to do the morally right thing at the expense of happiness?
The philosopher who first occurred to me when I thought about this question was Plato. In The Republic, Plato describes a city in speech to examine "what is just," along with other major ethical (and sometimes metaphysical) questions. To rule this city, he assigns certain particularly educated and wise people called "guardians" to lead over their people and maintain justice with totalitarian authority.
However, Plato points out that these guardians must never be corrupted. Thus, he determines that they must give up all private property and live in community bunkers so that their sole interest is in their people (an obvious parallel with Communism here, just an interesting note). They will have live with no luxury and the bare minimum of supplies. To this declaration, Adeimantus complains:
What would your apology be, Socrates, if someone were to say that you're hardly making these men happy, and further, that it's their own fault—they to whom the city in truth belongs but who enjoy nothing good from the city as do others? (419a)
This is a valid and intuitive complaint to many; even if the guardians have some satisfaction in completing their duty to justice, they still won't be very happy at all. Plato's main rebuttal follows:
In founding the city we are not looking to the exceptional happiness of any one group among us but, as far as possible, that of the city as a whole. (420b, and another parallel - utilitarianism)
Now then, suppose we're fashioning the happy city—a whole city, not setting apart a happy few and putting them in it. We'll consider its opposite presently. Just as if we were painting statues and someone came up and began to blame us, saying that we weren't putting the fairest colors on the fairest parts of the animal—for the eyes, which are fairest, had not been painted purple but black—we would seem to make a sensible apology to him by saying: "You surprising man, don't suppose we ought to paint eyes so fair that they don't even look like eyes, and the same for the other parts; but observe whether, assigning what's suitable to each of them, we make the whole fair. So now too, don't compel to us to attach to the guardians a happiness that will turn them into everything except guardians."(420c-d)
The rest of his argument is similar in style, his point being that happiness can actually drive one away from their duty of doing justice. Guardians that are too happy will be distracted from being guardians and tempted into gratifying themselves. Likewise, all who have the duty to be just must avoid being distracted by happiness.
I think this affirms your question of whether any philosophies are similar to your personal philosophy—Plato makes it pretty apparent that he believes people have a duty to do what is right (what is just, which is equivalent to him) even if it means they won't be very happy, although he does assert that the overall happiness of a city (and by his analogy, the soul) is best when it is just. This does not mean that the just person is always happy. As a matter of fact, he considers the path to justice very difficult, but sort of a happy ending story.
Another philosopher who occurred to me is Nietzsche. His views are similar to yours, but only marginally so because he differs in terms of what one has a duty to. A big theme in Nietzsche is the "will to power" and the "free spirit." He considers the best men to have a free spirit and exert their will to power as a demonstration of their superiority. As a philosopher, Nietzsche values knowledge and truth, although what he means by those terms, some argue, may be a little different from the common interpretation.
Regarding truth itself, Nietzsche says the following in section 39 of Beyond Good and Evil (Part Two, The Free Spirit):
Nobody is very likely to consider a doctrine true merely because it makes people happy or virtuous—except perhaps the lovely "idealists" who become effusive about the good, the true, and the beautiful to allow all kinds of motley, clumsy, and benevolent desiderata to swim around in utter confusion in their pond. Happiness and virtue are no arguments... Something might be true while being harmful and dangerous in the highest degree. Indeed, it might be a basic characteristic of existence that those who would know it completely would perish, in which case the strength of a spirit should be measured according to how much "truth" one could still barely endure—or to put it more clearly, to what degree one would require it to be thinned down, shrouded, sweetened, blunted, falsified.
This idea that the truth is often depressing is repeated often by Nietzsche, and something that suffuses his works is his idea that the free spirit is unhappy much more than the normal person. Although there is no mention of moral duty (Nietzsche would probably balk at the idea) or duty of any sense, there is a clear theme that Nietzsche's ideal man is far from happy (although he can experience times of pleasure). This is sort of similar to your personal philosophy, though I admit it seems much less noble (again, not really in Nietzsche's style).
Thomas Hobbes was a political philosopher who is often seen as the successor to Machiavelli; he focused on a practical and effective state as opposed to the ideal utopias of the past. In De Cive, Hobbes set the foundation for his theory of state, from which he determined what would be morally correct:
The Law therefore, in the means to Peace, commands also Good Manners, or the practise of Vertue: And therefore it is call'd Morall. (Chapter III, Article XXXI)
This is an important part of Hobbes' principles (you'd have to read his first three chapters to really get an complete understanding), and in short, it demonstrates how Hobbes considers anything in the pursuit of peace (as opposed to "warre") as moral, and that these pursuits are listed in his "naturall lawes".
Now, the second of these natural laws (derived from the first, which is simply that one must pursue peace or prepare themselves for war if peace is not possible) represents your very question of sacrificing happiness for moral duty:
But one of the Naturall Lawes deriv'd from this fundamentall one is this, That the right of all men, to all things, ought not to be retain'd, but that some certain rights ought to be transferr'd, or relinquisht : ... he therefore acts against the reason of Peace, (i.e.) against the Law of Nature, whosoever he be, that doth not part with his Right to all things. (Chapter II, Article III)
Thus, it is Hobbes' belief (expanded upon in his writings) that it is morally required for us to relinquish some of our rights (specifically, the right to whatever we want) in order to preserve peace. If anything we desire could cause conflict, it is our moral obligation to give up our desire and pursue the greater good of peace.
I think these philosophers would be useful in comparison with your personal ideas.