Totally fine to have sex! (Caveat that with unless your OB tells you not to - I had very small amounts of bleeding last time and was told not to until it stopped)
Late to this- but It is possible to have a yeast infection on the outside as well. Was diagnosed with this yesterday and it can lead to that same burning sensation. I would go to and OB! Urgent care and places like that won’t give you that thorough of an exam/know what to look for.
Re: First Trimester Sex