I think you should slow down. You are just out of a marriage, barely divorced. Most people need some recovery time, both to just settle down from the emotional upheaval of a divorce and to gain some perspective on what went wrong. Ending any marriage, even a bad one, usually requires a period of mourning. You didn’t get married to be divorced. You thought you were in love with your first husband. You apparently didn’t see warning signs. I worry that maybe you let yourself get caught up with the new beau so fast because you don’t want to deal with all the painful feelings that go with a divorce. New love is certainly a distraction.
The need for a green card is not a good reason for people to marry, even though it can certainly add pressure to a courtship. Your boyfriend is in too much of a hurry. I’m concerned that he gets heated when the issue comes up. I’m equally concerned that you don’t see that as a “red flag”. This should be a time of sweetness and romance. Instead, you are walking on eggshells.
If you were seeing me as a client, I would want to explore with you whether waiting at least 6 months might be a good idea. I’d also encourage you to get into some pre-marital counseling with your boyfriend so that the two of you could learn how to talk about something difficult without it turning into a fight. For a new marriage to work, you would ideally have the support of your family as well. I have a guess that they would feel much more comfortable if they knew you were taking steps to make sure you are making a good decision.
I hope this gives you a few things to think about.
I wish you well.