I'll tell you how it went for myself, maybe you can make yourself an idea. I didn't take anti-depressants although I was very close, but testosterone changed my life.
I was depressed for many years. I had a very bad year when I was 18-19, but I'm sure that the main reason for my depression was low testosterone. I didn't hit puberty until I was like 13 or 14. I was very, very short and I was very close to start a treatment based on hormones, because the doctor was worried already. I had very low testosterone back then and some doctors were monitoring (tons of blood tests mostly) my grown every three months. My mother didn't want me to go through procedure, so she slowed the process as long as possible and then, finally, I started to grow.
However, this low testosterone stayed for many years (I wasn't aware of this) and I had self-confidence and pride issues. I had this subtle and not very deep depression, but it was there, awaiting any little bad thing to sink me. A psychologist prescribed me anti-depressants and told me that I was the one to make the decision if I wanted to take them or not. The idea was to take them, try to get a better mood overall and then eventually drop them. I never bought them.
So, fast forward few years, I moved to a different country and all my personality flaws became bigger since everything was much harder. Self-love, self-pride, self-confidence issues, besides swingy mood and still same muscular development than since I was a teenager (none). I complained a lot, put lots of excuses, "nobody loves me" mentality, etc.
And then I started to lift weights, but had bad plan and nutrition at first, so it didn't really work. But then two things happened. One, I started to lift very heavy and eat a lot and second, I met a guy with a very interesting lifestyle based on pure positivism and he kinda taught me it.
And that was a huge change. Self-love, pride and confidence were automatically adquired. My mood became less swingy, I started to be honest with myself and fix things. No more excuses, no more complaining, just positive thinking with a very good attitude towards life.
So, if you can, just try to eat a lot more and do heavy compounds to rise your testosterone levels. Testosterone changed my life. You say that your mood improved, so it's a start. But try to really lift heavy, it'll do wonders.
You mention that you still felt anti-social at some times. I don't think that's related to testosterone though. I was very social back then (trying to fill my unhappiness with company?) and now I'm quite "anti-social". But that's because I'm an introvert and very picky about people. I don't like to have contact with people who don't share a similar mentality.
Also try to adopt this super positive mindset. It'll do wonders for you.
I hope this helped you.