If I've been married almost 7 years, am I entitled to anything?
Although I am legally married, we were never culturally married and remained financially independent. My husband is a medical resident and will start working as a physician next year. Although I did not contribute to his education or support him, I did sponsor his citizenship and got legally married (at 21 years old) instead of only getting engaged so he could get his working papers immediately. Through the citizenship he was able to complete his training to become a physician but 7 years later, I still have nothing. I feel used. Am I entitled to a part of his degree in terms of an asset?
You should consult with a divorce or matrimonial attorney. First, "culturally married" is irrelevant--the law only cares about whether you were legally married or not. So in theory, you would be entitled to some assets or support, but if you truly kept your finances independent, then the court (if you brought a legal action for divorce) might conclude that if you both contributed 50% to the marriage and both paid your own way, you simply split physical belongings down the middle and neither owes each other support.
IF it were the case that you supported your husband while he was in medical school, you'd have a claim to some of his earnings from his medical degree--but you say that you did not contribute to his education or support him, so you probably would not.
Note that if you earned much more than your husband has or likely will in the short term, you could be expected to pay support to him--though again, if the two of you were completely financially independent of each other, a likely outcome is you just both economically go you won ways.