That really depends on where you are going and where you are coming from.
In general, if you are going to a place that recognizes your union (civil or not, heterosexual or not), have paperwork to back it up, and have been sharing your life as partners for a while (ie shared financial responsibilities etc), you should not have any more trouble than non-ace couples.
Believe it or not, outside of weird sexually perverted cults like the Roman Catholic Church, having sex is not a requirement for marriage.
I can find no indication of “consummation” or other terms that’ that seems to necessarily imply sexual activity other than a reference to birth control.
Anyway, immigration proceedings are stressful and heartless. I definitely recommend making sure you know your rights and the process. I know money is tight, but if you can find an immigration lawyer that has experience with the immigration process of LGBTQ+ and other “non-traditional” couples that would definitely be a very very big boost to your chances.
I don’t know if “we don’t have sex” is going to count as a strike against you in a U.S. immigration hearing, but the lawyer definitely should.
What definitely counts as a strike against you is lying, and they are really good at finding out, so I don’t recommend you pretend your physical relationship is different than it is.