NO NAPS!

I am at my ends wits with my 2 month old! She refuses naps! And has been refusing them since she was like 5 weeks old. I have tried so many things and spent so much money trying to find things that will help her. She is formula fed I have changed formulas I have had my doctor test her for all kinds of medical problems but she is healthy as could be! She fights her naps to the point that she maybe gets a total of 2 hours a day just in naps! And it's not all in one shot. It's half hour here and there. But this baby is still so tired! That by the end of the day she is so overtired that she becomes a demon who screams and cries until she finally falls out! She goes to bed pretty early because her body just can't physically take being awake anymore! she is up every morning at 3:00 and stays up for an hour before finally falling back asleep and from that point on it's on and off sleep! I don't know what to do as I have tried everything from multiple white noise machines, swaddling with different fabrics, to rockers, bouncers swings and multiple carriers. Different pacifiers. I don't know what to do! She finally falls out after an hour of trying to rock her then leaving her in her bassinet to fuss for another hour or so. I don't know what to do. :(