Can I get my husband his papers if I’m 19 years old with a baby on the way?

Generally, a U.S. citizen may succeed in sponsoring a spouse in the immigration application for adjustment of status process, regardless of the U.S. citizen spouse being only 19 years old, but there are many other details that would need to be addressed in order to determine immigration eligibility. This includes, for example, information about a foreign national spouse's entry into the U.S., information about that spouse's immigration application history, etc. There really is no substitute for you and your husband consulting with an immigration attorney who, after learning all of the relevant information, could advise about immigration eligibilities, options and strategies, and could offer legal representation in the often quite complex application process.