My father applied for American immigration for me, and I went there. Can my son go?

If you and your husband don't get a license, then your father can only apply for you to go to the United States first. After you arrive in the United States, you can apply for green card status yourself, and only after you get approval can you apply for your children and husband. It's hard to say how long it will take. If it is fast, it will only be a year or two. If it is slow, it may take six or seven years. But the child will be faster than the husband. There is absolutely no need to change your surname. As long as you have a birth certificate to prove that you are the mother of your son and your husband is the father of your son, you can apply.