Although not politically correct, is totally fine. He/she does not like Chinese. In this country, private discrimination is allowed. I suggest you change your way of thinking and doing things as well. America is a place where people should respect abd be respected by others.
When I say that I don't need your help, that is what I mean and you should respect it. Why should you force your idea (in your own mind --- I acted out of goodwill) on me. When he said he did not need your help, just say leave or say "good luck" or "hope you feel better". Don't teke an extra step just because he did not take up your offer.
Learn to respect others, your life will be a lot easier. Just think what if one day you delined someone's offer, and that person kept on offering? ANNOYING