That sounds bunk, although I can understand the idea about wanting to treat your depression.
As for the depression, if it's clinical depression you can try a small dose of an antidepressant. Probably and SSRI. For anger, there's therapy. If the anger is difficult to control, a combination of medication and therapy might help over time.
Antidepressants aren't as scary as some people think the are. It really depends on what they put you on (newer ones are better), and the type. There's different classes of anti-depressants (SSRI, TCA, SNRI,). They don't cure it, but treat it giving you a little boost so that you can move forward. You still have to do the work on them. Sometimes you have to try a couple of different ones to find the right type for you. If it's not working after 4-6 weeks or you find that you get more depressed, then it's not right and time to switch. For most people, SSRIs work (SNRI if not). SSRIs can be taken at low doses, and most provide fewer side effects than other kinds. TCA and older classes are usually not prescribed these days as a first line of treatment (they can be nasty).
Anti-depressants don't change your personality, and they don't make your feelings go away. My ex gf was scared before she tried them, and then she tried after battling with depression and trying therapy, she started. She says it's one of the best things she's done. She feels more like herself, she hasn't had any side effects, and she's been able to breathe in life, and start enabling herself to move forward. I'm now on the same one as she is, and it works very well for me, too. (Celexa) She's doing therapy still, and finding that the therapy is helping her.
Taking an anti-depressant doesn't make you weak minded, or make you less of a person. Depression is physically visible in the brain, actually, and can be very debilitating. Clinical depression and the "blues" are different, btw, and an anti-depressant isn't recommended for that. So, you're doctor will have to evaluate you and see if you have clinical depression or not.
I would talk to your therapist (or another one you find) about the issues, how they are interconnected, and make a deal that you'll work on the depression and anger with transitioning.
Getting help with your depression may help you to transition more easily, and make it over different obstacles in the process. Help with the depression may or may not need meds. Therapy is a good first step, and medications if necessary, since meds aren't candy and they won't work if you don't have clinical depression.
Good luck!