If doing good deeds makes us feel good and forces us to do more good, are we now doing it for our own feelings or for the actual good? If the former, then are we being selfish?
Yes every act you do is selfish even if it is for altruistic purposes. If you help a homeless person by giving that person money or donate money to a charity you can say that is altruistic, but you probably get a good feeling from doing that. Which is why perhaps you would do such a action again because it causes you to have a benefit ie feeling good rather then bad. So unless you can find a example in which you do something that benefits someone else that does not give you some sort of benefit then we can say all actions upon other are in some way selfish.
Man does not seem able to “help” his selfishness; it seems to come from his animal nature. 
Freud discovered that each of us repeats the tragedy of the mythical Greek Narcissus: we are hopelessly absorbed with ourselves. If we care about anyone it is usually ourselves first of all. 
Human beings not being selfish is an unrealistic idealism. "I am selfish because i want to feel good and i earn this good feeling by helping others" is the best man be in terms of benefit to others.
 The denial of death (1973), Ernest Becker
Every action is done with a purpose. If there is craving or expectations from any actions then it's ego. Ego is created or observed whenever there's an outcome of the actions. Suppose while playing ping pong the nature of the player would be to score every time & win the game. Instead playing the game without intention would be more joyful than the sense of happiness over winning the game. The happiness & sadness are part of the ego. Another example is, preparing for exams to score good grades, that takes the focus from understanding the subjects to scoring well in the exams. The essence of playing ping pong is joy, while that of exams is to know how well the e subjects are understood. The purpose always has to be staying in stable state of mind, then the deeds are done automatically, without knowing or labelling them as good or bad.
Depends on your definition of selfish.
Man has a limited time of existence. Any deed he performs must be valued against other deeds that may be performed at the same time. Once a particular point in time has gone, he can no longer act upon an action at that given time. He must decide and place a value upon differing actions that he may undertake at a given point in time.
Do I want to do this now, or that now? Whichever one decides, is the one decision one valued more, at a particular time.
Is the valuation of actions and acting on the most valued action considered selfish?
I attempt to write an answer from a different angle from the other answers already supplied here. The issue is to do with language.
There is the term enlightened self-interest. Then there is the term selfish.
Most/all good deeds are indeed self-interested. Some ethical systems often purport a reward for ethical behavior at some point; pleasure, in whichever form, is rewarded at some point.
However, the term selfish is more ambiguous and can mean both self-interested and unethically serving one's self. However, the term is generally taken to have strong negative connotations.
All creatures are seeking pleasure/happiness in one way or another throughout their life. Even sadists seek pleasure; but they get it by hurting another person. If so, why didn't you say bad deeds are also a part of selfishness?
Those who seek stability of mind are less in number. I am saying so because most people will have a tendency to seek pleasure even when their mind is in a 'stable state' even it is only for a short time.
You may define the word 'selfish' as Someone who thinks only of their own advantage: According to the meaning given, a selfish person does not think of others' advantage. (The word--'only' implies so.) But good deeds of people are done thinking of others also. So it is not sensible to call such persons selfish.
The meaning of the word 'own' in the given meaning (of 'selfish') becomes fully subjective and often makes big differences if you try to define it. Some people see others as their (own) fellow beings. And some others see their own self everywhere. See Geetha 13.28. When we view such people from a low level we may say so. But there are people who are in a higher level than what we think. In their case there is nothing to increase or decrease. They are beyond good and bad, happiness and sadness etc. So, in their case your opinion fails. Anyway it is not good to say good deeds selfish even though there is a scope for saying so.