Ohshitwhatnext you aren't the problem here 
I had an emotionally neglectful upbringing. Physically and financially all my needs were met, but emotionally there was nothing. I've done the depression, I've done the anxiety that so often goes hand in hand with it, I've done the suicidal thoughts, I've done the sitting on the knife edge of suicide...and I too backed out. One little thing changed my mind and I'm so glad it did.
I got help, by doing exactly what you're doing and speaking to my (absolutely fantastic and I owe her my life) GP. I too was at university and the help and support from them was amazing. They provided me with "6 weeks" counselling - I was going there for 18 months - again, that counsellor played a huge part in my recovery. I had support from student services, I had a mental health mentor, it was absolutely fantastic support wise. It all started with that first, very difficult conversation though.
Fast forward to now and I'm genuinely happy. I do a job that I love, I have a husband that I have had a fantastic relationship with for the last 10 years (we met at my absolute lowest point and he's been there every step of the way), we're about to have our first child (on Wednesday, eek!), and probably most importantly, I've learnt that it's ok to scale back, and in the case of my mother, even cease relationships with those who have a negative impact on my well-being.
You're going to be doing the hardest bit today, but it will get easier. Be kind to yourself and maybe have a little treat ready for after your appointment, whether that's grabbing a fancy coffee or hot chocolate on the way home, a lazy luxurious bath, whatever - implement some self care - it's important to be kind to you 