I started T a year ago last month, but I was on a half dose. I started a full dose around September/October of last year and since then I have been going pee a LOT more often. Now, it's literally every other 20 minutes or so I have to go. I do drink a lot of fluids, but it's never been this often.
Is this something common for people on T? My friend told me she read it was common for women in menopause, since they're losing estrogen. Could that be the case here, since I am losing estrogen as well?

This is something you need to discuss with your doctor. It could be nothing but it could also be a sign of diabetes or a UTI. Without a few medical test to check for these conditions, you can't be sure what is happening.

Agree with Dena. It could be a sign of a lot of things, so it's best to get it checked out. I would call and bring it up before you're scheduled for your next round of blood work and see if there are any additional tests they could order to look into it.

I may have peed more when I started T, but I already peed a lot as is. I have a small bladder and I drink a stupid amount of water per day.

You need to talk to your doctor. I did notice an increase in the amount I peed (I was on T for 3 years, lost it for a year and went back on three months ago) but it wasn't so much that I am in the bathroom constantly. I drink a lot of water as well as tea and coffee, but if I was going to the bathroom every 20 minutes I would certainly call my doctor and ask them if it should be expected.