Is it possible that I might do a good thing without consciously reasoning it? Sure. I would say this "doesn't count" for me choosing to do a good thing, though. How could it? This would be more of an accident-serendipity kind of thing.
That still doesn't change the fact that when I choose to do a good thing, I do it because I want to help others instead of hurt them. And that I do not choose to do good things because it's going to make me feel good.
It depends on what a choice is. When does a choice happen? Some, small, evidence suggests we make make a decision before we make a choice, where 'choice' is the conscious experience of making a decision. In a sense the experience of choosing is the rationalization after the fact of deciding.
You neurons don't want to help others, neither do the clusters of neurons. At some point up the hierarchy of consideration a 'desire to help others' emerges - but that 'desire to help others' is almost certainly built upon things doing stuff without consideration of others per se. The pathways in your brain that lead to your decision to help others were shaped by reward/punishment trials in your past. Helping others has proven socially useful, which has reinforced the behaviour. The reinforcement process occurs using such things as neurochemicals which have the advantage of acting on multiple neurons over a period of time.
So while 'you' - the consciousness - 'chooses' to help others because 'you' want to. 'You' only 'want' to because of mindless things lower in the hierarchy weighing the possibilities at the time. Whether it makes 'you' feel good is not necessarily the only consideration. Its whether the behaviour is positively reinforced as a result of the consequences of your helping.