Sick Savannah.... Help A.S.A.P please.?

Okay here are a couple things to help you guys diagnose what COULD be wrong with her(They say it's a she but not too sure because it is hard to at the age it is) She is a 6 month old Savannah w/ 20 gallon aqaurium style tank w/ mesh lid. She has a 100watt daylight spot basking bulb with some UVA in it(6% or something) She has a half log, coconut fiber substrate(2-3 inches so she can dig) and a large water dish on the cooler side. I plan to buy her a UVB bulb but I am not sure if she will even live that long :/ I bought her 2 days ago and the owner said she was on a daily feeding schedule and very healthy, and aswell she looks healthy. The thing is though, she is ALWAYS sleeping and when I go to touch her she runs away.. am I doing something wrong? Do I need to buy that UVB bulb? Is she sick? Help me please. Btw I run the light for 12h during the day then I turn on a under tank heater for nighttime. Her temps right now are at 88.4 and still rising up (I have a digital thermometre and the probe is suctioned to the hot side of her tank).