When my system ran primarily on Oestrogen, I was in one of a few states more often than not. Agitated, frustated, stressed, angry or a combination of the three if I wasn't feeling empty. In my instance that was a characteristic of the depression and anxiety that I had. Even after a few months of therapy my mood was unstable at best, I'd have arguments with my mother over little things like what was for lunch. After starting Testosterone, arguments turned into discussions, agitation turned into a tolerable level of anxiousness, stress and frustration dissipated significantly and anger mostly dissolved.
It wasn't all sunshine and roses however, where Testosterone made me feel a lot better in general, it didn't stave off the symptoms of depression and anxiety. I dealt with them in a more constructive manner sure, but the lows I felt seemed to be worse, perhaps because I felt positive emotions more often. I'm now on SSRIs to treat my anxiety and depression, and that combined with Testosterone has made me a more pleasant person to be around. It didn't make me any more assertive unfortunately, I still have the spine of a sea cucumber, but that's something I'm working on along with self confidence and esteem.

All things said, my experience is likely different from many others simply because I'm not you or someone else. Perhaps once you settle into HRT, your mood will become more stable. The gym sounds like a good place to direct any potentially negative energy, and will help with strength/fitness should that be your goal. I'm looking to join one too, mostly because I need to get in shape and want my physique to be more masculine. All the best!