Ive had the same thing pretty much all my pregnancy. Im 38 weeks now. I figured if he used a condom it didnt burn as much. So we've been using those. Other than that u can clean u self up right away afterwards with lots of cold water. Thats always helped me.
Ive also noticed that it hurts the most if u r dry down there, which was quite a problem with me, especially as the pregnancy progressed so try to keep urself moist. Weather its with lube or what ever is comfortable with you.
I hope this helps. Ive felt the burning and I know its very painful. Good luck.
Try using petroleum jelly down there
Your lady parts can swell during pregnancy which can cause discomfort. I'm not sure about burning necessarily. I haven't experienced the swelling, that I can tell, but it's very common.