With the breakthrough technology and significant improvements with current testing, 3 months post exposure is sufficient time for you to test and conclusively rule out hiv. Getting to your doctor is the first step. Discuss your concerns and he'll take care of you.
Condoms are usually durable, however old condoms or those exposed to other conditions could compromise the condom. In the future, why don't you buy your own pack. It's a good idea to give the partner a condom yourself.
No, you can't tell in the heat of the moment if the condom breaks. Most won't but you need to get into the practice of periodic inspection. You can do it conspicuously, whereas it would make you feel very comfortable.
The ultimate scenario is protected sex with an individual who is in a monogomous relationship who shared his recent results with you. Think about it!