I think you should go to an anti aging doctor or at least go to the TRT section of this forum and learn everything you can, including what labs you need before making this decision. TRT can help depression and social withdrawal for people who are suffering from hypogonadism (resulting in low testosterone levels and other hormonal imbalances) but without any blood work it is impossible to say if this is your case as depression can have many many causes other than low T.
So taking testosterone (a full TRT protocol, actually) may or may not be what you need and if it’s not you would just be blindly playing with your hormones and risking ending up worse than when you started.
Good luck and I hope you find the way to get better.