My experience is that it takes a while to get a counselor on the NHS, with long waiting lists. Has your GP referred you yet? When you say end of uni, does he mean the current term or the end of your degree?
TBH, I'm not sure I understand why the GP would want you to wait. Counseling is normally and hour once a week, so not like it would take up a load of time. It can be upsetting sometimes, sure, but at least you'd have someone to talk to.
Have you got a partner or friends who know/understand how you're feeling? It makes a huge difference. I've got a good friend who has pretty severe mental health issues including depression, and we both say that at least having a friend who 'gets' depression is very helpful. Some people just won't understand, because they've not experienced it. My husband also struggles with depression/anxiety, so I know he isn't judging me for my off days/weeks/months.
Can I ask what dose you were taking before and what you're on now? I started citalopram recently, and it did nothing at 10mg, but started working at 20mg. You may even need a different drug altogether.
I'm not sure what to say about you not leaving the house, other than I completely understand what that's like. I didn't want to see people or be seen. At one point I suppose you could say I was a bit paranoid that people were looking/laughing at me, or that I was annoying people. When DH did force me out of the house, I found it hard to talk to anyone, just in shops to ask a question, and I'd mumble or talk so quietly they couldn't hear me.
Take any small victory you can. Even if you get out of the house for 10 minutes to walk to the shop and buy a tin of pop, you've done it.