It's not uncommon. There may be some kind of irritant involved. Have you changed condom brands recently? Many people are allergic to latex but there could be something in the lube on the condom that is bothering your skin.
More than likely the tearing was caused by vigorous activity. Be sure to use lubricant if you start to chafe during sex. (as with all things, do some research to find a hypoallergenic lube! K-Y is probably pretty safe) I have dealt with issues like this before as my skin is sensitive all over my body.
Yes, it could be multiple tears from trauma. It is also possible to have an allergic reaction to Latex condoms.
You may end up with a bacterial or fungal infection because of this, unfortunately, because the broken skin can let in infection. You can get relief with Vagisil. It has an anesthetic. You can get it at the drug store without a prescription. You might also want to get some Azo-Standard medicine for bladder infection pain just in case, just to have on hand. If you have never had a UTI, it is a lot of pain with urination. Burning, stinging, frequency, urgency, can't sit still pain. Azo-Standard is only an anesthetic and does not cure the infection though. If you get a UTI, you will probably need an antibiotic. It's not a given that you will get a UTI, but it is very common. It is not the same thing as the trauma you are describing with little cuts.