The only reason that medical bills and supporting a family are even questions is that he values his family's well being more than he does that of someone who might be helped by charity. Phrasing things in utilitarian terms, he puts a much higher utility on his family than on a random person. As such, he should only donate to charity once he has spent enough money on his family that the utility from doing is, per dollar, so much less that that factor overwhelms the large multiplier that he gives for his family's welfare compared to a random person's. Given his description, he clearly hasn't reached that point yet, so he should spend nothing on charity.

This leaves guilt (or warm fuzzies, which are the flip side) as the only reason to spend anything at all. The rational amount (ignoring questions like "what utility to I get from assuaging my guilt") is zero. Take care of your family, who needs it, and stop feeling guilty for not donating.