I have been diagnosed with a cyst on my lower lumbar/thoracic spine. Its hitting nerves in my lower back. Do I need to worry about getting surgery?

Maybe. There are different kinds of "cysts" but the most common "cyst" in the lumbar spine that causes is a pinched nerve is a synovial cyst. This is and inflammatory cyst that causes symptoms of a pinched nerve. Surgery is sometimes indicated for large, painful cysts that are unresponsive to nonsurgical treatments like pt and injections.
Depends. If you are referring to a synovial cyst then surgery can very often relieve your pain. A synovial cyst is an inflammatory cyst originating from the lining of the one of the joints that makes up the spinal column. They can compress a nerve and cause pain consistent with a pinched nerve.
If tarlov cyst. Tarlov cyst do not cause symptoms there removal is fraught with complications a tarlov cyst is just a MRI finding ther is no treayment that produces a better outcome best left alone in my opinion.