How do I get her to go to sleep??

I have a 3 month old baby girl, she was 2 months early, so her corrected age is really 1 month but she's more like a 2 month old with regards to development. Anyways, she just will not have naps. Today she was awake from 10am-5pm and was very fussy, screamed in the end for about 1 1/2 hours. I've tried gripe water and ovol for colic, and those don't work. She did this yesterday too, and then slept for about 5 hours. Then she was awake again from 3am-7am (although that time she was just making happy noises in her crib) The doctor said to let her just cry herself to sleep but I don't have the heart, I will try for 15-20 min and she just doesn't calm down. Can anyone help?? I am going crazy.