The feeling of good (which can be physically observed in brain activity) is itself the reward for doing a 'good deed'. Therefore, there is no such thing as a purely altruistic action.
Lots of people either inherently lack or actively suppress the capacity for feeling good for altruistic actions, and in fact do not feel "good" for doing a "good" deed. Your argument faces further difficulty when you consider that many people feel "bad" if they do not do a "good" thing - if they were self-rewarding, they would feel good regardless of if they pursued or passed on an altruistic action.
You're arguing for psychological egoism, a field of philosophy widely critiqued for being founded on a circular argument - it rests on the idea that people only do things that they enjoy or benefit them, and then concludes that any act someone takes must be because of those reasons.
Even if egoism is true: consider how abstracted from any sort of concrete moral decision one must be to say that, because some people feel good for doing altruistic things, that invalidates the morality of that altruistic action. "You did something that made someone else feel good, and seeing them happier makes you feel good, and you have generally improved the state of the world in some small way, but because you have any positive or negative thoughts or feelings regarding this situation you have thus invalidated your own actions".