This is easy. The "philosopher" you're interested in is Ayn Rand and the philosophy she created is called Objectivism. No one is better at defending selfishness than Ayn Rand, and she has quite a loyal following among libertarians. Her sole book I own is The Virtue of Selfishness and I personally couldn't stomach finishing it. That being said, I'm going to respond to your question as an absurdist who fundamentally rejects Ayn Rand as a charlatan.
Your irrational guilt is rational insofar as its a product of biological evolution. According to sociobiology, we have a genetic heritage which predisposes us to biological and psychological altruism. Caring about others serves to make us social creatures, and eusocial impulses and behaviors, along with language, have given us virtual dominion on this planet. There are certainly psychopaths and sociopaths who don't wrestle with any form of guilt, but the vast majority of us feel guilt, and it's not to hard to figure out that if you put $100,000 in the bank instead of send it off to feed, clothe, and buy medicine for children in a war torn country, and they die, you are in some nebulous way guilty of negligence. The doctrine of supererogation was cooked up to help us cope with this guilt. Martin Luther split the church in half because he opposed it. Thus, the "irrational guilt" you feel with has a deep and colorful history.
As an absurdist, let me just offer you some philosophy that might help you come to terms with your guilt. First, as Ayers held morals aren't about reason ultimately, they are about feelings. This doctrine of non-cognitive emotivism essentially suggests that no matter what philosophy you "cook up" to try to assuage yourself of guilt, you're just trying to pretend something about yourself that isn't true. Absurdism, if you read Camus carefully, sweeps aside all of the fancy philosophical doctrines as elaborate rationalizations. Thus, if you feel guilty because you know that you could do something to save dying children and you don't, well, you can find whatever argument you want to justify not feeling guilty, but that may not convince you deep down inside that you aren't allowing children to die. This would be a form of self-deception. Because honestly, you are allowing children to die. Anyone who has any means and spends it on frivolities instead of sending it to help others is guilty of that, and that's anyone who makes more than what they need to survive.
The Christian mythos purports that God incarnated a son, performed a child sacrifice, and thereby absolved you of guilt for all sins, and letting children die by being selfish certainly qualifies. Therefore, if you are a Christian, you should find some comfort in that your original sin, your preference for your selfish behavior, in this instance, letting children in a foreign country die, will be forgiven by your maker. An absurdist, however, would point out that this is a scam just in the same way Objectivism is because all of the argumentation presented to you is just rationalization. It's pretending that a fancy logical argument is going to disabuse of your biological constitution to feel guilt when you are involved in causing through inaction others' suffering.
An absurdist, then, will simply you encourage you to accept that you are selfish, your selfishness does lead to others' suffering, and that no fancy doctrine, high philosophy, or logical argument will ever substantially change that. Just like you must accept that you will someday die, and that nothing you do has any grand cosmic significance, so too you are selfish and your existence and choices come at others' expense. To follow Objectivism or Christianity or Kant's Categorical Imperative all amount to a bunch of philosophical hooey to buy into a linguistic snake oil with the sole end of deceiving yourself.
This, of course, is not a justification to be selfish. It is a recognition, that like death, it is something you cannot prevent; at best you can influence it. You eat your vegetables and go for a run, you'll live longer; you donate some of your time to some needy people in your neighborhood, you'll feel less guilty. But you are neither immortal nor do you lack basic human decency, so you have to accept that you are simply limited. By embracing that, the guilt doesn't go away, but it doesn't distort your thinking. In fact, it makes it easier to see the distortion in thinking by the charlatans who promise you if you only believe in their philosophy, doctrine, or good book, you can find salvation. Ultimately the price of clear thinking is uncomfortable truths. Being an adult means accepting reality as it is, not as you want it to be.
So, read the Virtue of Selfishness. Maybe the words there will convince you it's not immoral to be selfish, but if you have any critical thinking skills, you'll find that what she is selling doesn't fundamentally absolve you of guilt. Nor should it. If you have the means to save lives and reduce suffering and you instead spend your time with frivolous entertainment, you are guilty. We all are.