My resting heart rate is between 110 and 120. Is this normal? I am 5'9" and 120 lbs., 34, female.

No. It is not normal. It can be a side effect of quetiapine. A search for other causes is reasonable: thyroid excess, anemia, fever, infection, emotional upset, and pain are typical. More ominous causes include av fistula, congestive heart failure, or sepsis. A 24 hr heart recording would be helpful (to see your hr during sleep).