Low testosterone and under active thyroid

Im 38 yrs old and have low testosterone. My doctor gave me testim to take and its working very well! But with all the side effects i was wondering if there something safer out there to take that would work as well as Testim? Right now Testim has changed my life for the better but im worried about long term effects like hair loss.I read that taking external testosterone will likely zero out my bodys own natural production .Does that go for all types of testosterone thearpy treatment? Should i worry about this? All i know is that i feel incredible takeing Testim! My sense of humor and personality is back! I can actually handle a full day of work without crashing. I'm getting great results while working out!My doctor wants me on testim for the rest of my life. I dont know if thats smart thing to do. If i stop takeing testim right now will my body start producing testosterone on its own? And are there long term side effects? Im also being treated for an underactive thyroid. I was takeing Levothyroxine but i was geting terrible side effects. Could not function at work .So i stoped takeing it and feel so much better.Now my doctor wants me to try takeing half a pill a day. My question is Can an under active thyroid and low testosterone be linked? They both appear to have the same negative side effects. If i get my thyroid taken care of will that help my body to produce normal levels of testosterone with out takeing testim? Im so confused and not geting any answers!Thanks! Joe