You should be able to have sex up until labor if you want, it can become uncomfortable for some, others still enjoy sex. Never should it burn, pregnancy sex is not the cause. You might have UTI, yeast infection, or something else. Call the ObGyn.
Sounds like you need to see your Gyn/Ob. You could have an infection. Best to get it treated before it affects the baby. You are still 13 weeks from delivery, so you should still be able to enjoy Intercourse.
unlikely to be an STD, but kind of semi-likely to be a UTI. my mom has been pregnant 5 times, had the same problem with both of the last 2. once it was a UTI. the other, she was farther along in the pregnancy than they realized. check with your doc. Yeast infections are more likely during pregnancy than UTIs, though.
You might have a bacterial vaginosis infection (BV). No worries it is very common in pregnant women, but there is a very slight chance that it can cause premature delivery. Schedule an appoint ASAP, and check. BV is very common in pregnancy especially around 23 weeks. http://www.cdc.gov/std/bv/stdfact-bacterial-vaginosis.htm the link may help.