If you are really worried about HIV, you can make an emergency appointment with your local GUM clinic and explain what's happened and ask if they can give you PeP.
From what I've heard it has pretty gross side effects so weigh up the pros and cons before making a decision.
FWIW I've had condoms split on me 3 times now and I've never gone for PeP. My tests have always been clear. However if the client was from a high risk population (intravenous drug user, has sex with men, has regular bareback sex with other sex workers) then I would probably choose to do so.
Please remember that most STIs are completely curable with antibiotics - it's just the fact that they are sexually transmitted that makes them a really big deal. You'd feel comfortable telling people "I've got tonsillitis so I can't work" but you'd never tell someone "I can't work right now as I have chlamydia."
I'd suggest with your BF, tell him you've been to the GP as you had pain in your ear/throat/kidney and you've been diagnosed with an infection in your ear/throat/kidney which means you need to take antibiotics for the next 2 weeks. This will mess with your contraception method, so you'll have to use condoms for the next 2 weeks, or just not have sex at all.