Are you still in peri? My provider told me that it was possible I'd need to go up a notch on my patch once I was post-menopausal and what piddly amounts of estrogen I was still producing stops. If you're running solely on the patch's estrogen now, that might need to be supplemented. I agree with the idea of taking an extra patch and adding a little extra to see if that helps? I've done that, and that is how I know unequivocally that .1 is too much and .05 is not enough.
Personally, I wouldn't even entertain an anti-depressant if an estrogen increase will do the trick. And old doctor of mine was VERY resistant to my going on estrogen and pushed anti-depressants. While I get they're helpful for many women, oftentimes they're used as a first-line treatment (gets us out of the doctor's office quickly!) when they shouldn't be. IMO. As always, YMMV.
Good luck! I know this is tough.