Is it possible that certain medicines can give you insomnia? I began taking a medicine for inflammation in my ribs, and a few days after I started taking it, I began having a lot of trouble sleeping. I've been awake for about 48 hours now, I feel groggy and fatigued but I just can't fall asleep. The medicine said nothing about sleeping side affects, so I'm not sure if this is normal or not.

Absolutely some meds can cause insomnia. Are you having pain? That also can cause trouble sleeping.

BTW, very cool avatar.

Yes, absolutely it is possible. Your doctor should have made you aware of the potential side effects of the medication before putting you on it.
If s/he did and s/he did not mention insomnia, you should DEFINITELY talk to her/him about this immediately.
You should talk to your doctor anyway, as it is not healthy to have insomnia.