Personally, I've been on T for nearly four months now, and out of all of the effects that I've experienced, I wouldn't list 'anxiety,' as one of them. Believe it or not, before I started T, I worried about this too because I was on anti-depressants (Used to treat my severe social anxiety,) for years. I was afraid that the T would cause my anxiety to return, but so far, no such luck - which is awfully good! In fact, for me, my anxiety is more controlled than ever before. Now, I don't know about you, but I think that in my case, my social anxiety stemmed from having gender identity issues without knowing about those issues. I was so uncomfortable in my skin that it cause me panic attacks, and I believe that now that I feel more comfortable with myself, it's going away even more.
However, this is not to say that you might not have a spike in your anxiety - especially because I don't know what kind of medication you're on. When you go in to get on T, your doctor will ask you if you're taking any medication, be sure to let him know, and they'll probably be able to tell you if there are any common side-effects that the two medications might create or if they're even safe to take together.
Other side effects ( Physical or mental, ) are going to differ between person to person. For myself, the first mental effects that I realized was just an overall feeling of confidence and becoming more comfortable with myself. I was and still am more at peace with myself than I've ever been. I've heard of some transguys saying that they've become more aggressive, but I never experienced that. I've also realized that my weeks tend to go in cycles; I take my injection every Sunday. Monday and Tuesday are my extremely happy and hyper days, I'm so energetic that I feel like I could climb a mountain barefoot. By Wednesday and Thursday, I'm quite mellow. By Friday, I'm a little rundown, and on Saturday, you just don't want to have anyting to do with me. And then it starts all over.
Also, the only supplement that I was ever talked to about is something called Chaste Tree Berry. You can buy it at health stores, like Wild Oats, or Dave's Nutrition. It's something than menopausal women take, believe it or not, but my doctor prescribed it to me because it helps lower estrogen levels - which is obviously what you want when you're taking testosterone. So that might be something worth looking into. Plus, it's over the counter, so that's a plus.