There is a "morning after" treatment.

If you think you've been exposed, get thee to a doctor or clinic, ASAP! Have your partner come with you if they're willing.

Depending on the risk (and how long you've waited), the doctor may put you on a course of HIV drugs for a month or so. Not fun, but sure beats the alternatives.

This can also be an option for "we forgot the condom".

Just realize that the doctor may get tired of seeing you in their office every few months. Condoms don't break that often.