Why wont my baby sleep?

I feel like she's fed enough and her cries also sound like she's exhausted. I have been trying to put her to sleep around 8 or 9 for the past 2 and a half weeks. She never cries from a wet diaper. We try playing relaxing sounds and give her her pacifier. I'm just really exhausted and haven't had much sleep in those 2 weeks. She's almost 6 months and also has her 2 bottom teeth about to come in. Some nights I had given her infant tylenol. It seemed to help, but I don't want to give it to her because I'm not 100% sure that she's in pain(from teething ). I used to have such a set schedule for her but now its all over the place with her crying like this. Some nights i have to nurse her to sleep and I'm pretty sure she's just sucking for comfort. Some nights when I put her down to sleep she acts as if she just wants to play and have fun. I really want to try the cry it out method but I'm not 100% about it. I just don't know what to do anymore.