If the condom was used accurately, was a latex (not "lambskin") condom and did not break or tear then (even assuming your partner was infected with chlamydia and/or gonorrhea) neither of these strains of bacteria can pass through a latex condom barrier.
This OBY-GYN is just guessing at this HSV business. In addition if there is a concern for bacterial based STD's such as gonorrhea or chlamydia then testing for these can be done rather soon after the intercourse. Bacteria specific to both these STD's would confirm these diagnoses.
From your posting I'm going to assume that testing was done and you're waiting for the results, right? Sorry; opinions from this forum don't really mean much.
Has your boyfriend been tested for any STD or exhibited any symptoms such as a discharge or burning?
No, you can't "fix" this. Your immune system is likely to take care of the issue on it's own as it does in many cases. You continue with your normal OB-GYN follow up visits as usual. And of course you can have children.
You tell your new partner whatever you want to tell him. Perhaps he's the one who gave you the HPV (there's no real test for males).