I came here illegally I married a US citizen but I’m not sure if I should apply for deferred action or through him?

If you are married to a U.S. citizen, he can petition you for a green card without you having to apply for deferred action. Also there is no information given to determine that you would qualify for deferred action. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case, advise you of your options and, if possible, make sure that the necessary paperwork and documentation is presented so as not to delay the process.

If you entered the US without inspection, you cannot adjust your status without proving extreme hardship. You should consult an immigration attorney about that. If you entered before your 16th birthday, you may qualify for deferred action, which will provide work authorization but no other legal status.

There are BIA cases that define "extreme hardship." Matter of Pilch, Matter of Anderson and Matter of O-J-O. You need to consider the timing of things since you are pregnant. Deferred action, if approved, allows you to stay in the U.S. but if you do consular process and the provisional waiver, you can get permanent residency.