Inversion therapy is a form of exercise, where you go upside and enjoy. No sweating, just relaxing. Keep drinking plenty of water and smelly urine should go away.
When I first started inverting, I was losing lot of hair while combing. Its gone now. My hair roots have become stronger and dont shed that much. So, just keep at it.
How long do you invert? Do you do full inversion. You should also try some exercises like turning neck from side to side and twisting the entire torso. Helps in increasing the flexibility of spine, which is our main motto here.