Severe pain in back. Some pain and tightness in chest and shoulder pain. Took Advil (ibuprofen) and pain has subsided. Could this be a heart attack??

Maybe not. If the advil (ibuprofen) improved your pain it is most likely some sort of inflammation or muscles or bone contusion. Unlikely advil (ibuprofen) would improve pain from a heart attack. Also your age of 33 and a female would make it highly unlikely that you are having a heart attack.
Possible. Women are notorious for having atypical symptoms during heart attacks. It doesn't sound typical and usually isn't relieved with Advil, (ibuprofen) but it wouldn't hurt to see your doctor for evaluation to be sure. If the pain recurs tonight and is severe, ER/911.