When my babies are three months old they usually took two naps during the day...one in the morning and one in the afternoon. They didn't sleep through the night though.
My third child never wanted to go to sleep at night even tho she was tired and well rested from naps so that she as not over tired. I used to stay up with her until 3 am every single night and it was exhausting. By the time she was ready for the crib, she would make herself throw up every night because she didn't want to go to bed. The doctor finally had me give her benedryl when she was ready for bed to get her on a sleep schedule.
So I know your pain. When she wakes up in the morning, keep her stimulated and well fed. Then let her take a couple hours nap. When she wakes up, keep her up, don't let her fall asleep. Let her nap again in the afternoon. Don't let her fall asleep when she awakens again.
It will take time before she settles down with a new schedule, but it will be well worth it for her and for your sanity.
Here is a link to a chart which will help you in keeping her on a somewhat stable schedule.
http://www.babycenter.com/0_chart-how-much
-sleep-does-your-child-need_7645.bc
Good luck.