If you feel they're changing you, you don't have to keep taking them-just give them a try, and see if it improves things.
Actually, no. If you feel like they're changing you in some really negative way, you go talk to the doctor who proscribed them, just like any other prescription which starts having unexpected side-effects. If it is something which is normal with the medication, they can help talk you through it and let you know what to expect. And if not, they can likely offer alternative medications to which you won't have that sort of reaction.
Stopping medication without consulting a doctor can be just as dangerous as self-medicating, especially with things like antidepressants/psychiatric drugs, where you're suddenly removing some neurologically inhibiting or stimulating chemical from your body (with which it had previously had enough time to start adapting to). For antidepressants, that tends to come in the form of severe waves of depression. There's a reason the phrase 'off your meds' is synonymous with 'crazy.'
I don't see anything demeaning in taking antidepressants to end depression. I personally think you should definitely go for it.
My problem is that I'm not sure if it's even necessary. Like, if things are going OK in my life, then yeah I feel ok and good. It's just that I just hate my lifestyle and my loneliness, so I'm just always morose and negative.
EDIT: I do feel like an OK person, just that I'm stuck acting like a depressed person due to my circumstances.
And yes, you should see a doctor about depression if it is, in any way, inhibiting or crippling your ability to live the sort of life you want to. Getting sad or anxious from time to time is normal and should be expected in life. Staying in your apartment most weekends embroiled in a mix of anxiety, sadness, guilt, and self-loathing over staying in your apartment doing nothing all weekend, on the other hand, is not something which should be expected or become normal as it is actively making your life awful.
Keep in mind, your brain is itself an organ made of tissue and cells like any other. Taking the 'artificial' way out shouldn't be stigmatized or thought of as 'the easy way out' any more than antibiotics or surgery. When it comes to clinical depression, you can't really will it away any more than you could will away an infected tooth or a bad back. And that's why your therapist is suggesting seeing a doctor about medication: they have observed you and decided that the universe has decided to fuck with you in a way that, through no fault of your own, you have no control over.