you discover the condem broke??

There are 2 issues here:  
1) possible pregnancy  
2) STDs
If the lady is using backup birth control, then non-issue.  If not, she should use morning after treatment.  Next Q:  Who pays?  I often have ladies handle filled condoms with great care, sometimes even check for leaks which was freaky.

STDs:  hopefully both parties are clean.  Both should be retested ASAP, but probably no reason to freak out.
skb

when either a condom broke

or

we got caught up in the moment and coupled au naturel

First - I get tested every 3 months. So I compare notes with the lady about birth control and her frequency of testing and status.

With a civvy I would consider birth control to be my responsibility but with a professional I consider it to be hers. However I want to know! And to take plan B if the situation is not covered.

Then I immediately get tested again and refrain from any bare activities until I receive my customary clean bill of health.

I would be *much* more concerned if this was a zipless fuck with a civvy than I would with a provider...