Can you convince me to finally go to counseling?

So I feel like I need to go to counseling to sort out everything in my life. I’m in university, and the counseling center is free. Plus it is fairly easy to make an appointment, not to mention how convenient the location is. I wouldn’t say that I have major issues that I need to talk about. I mean I’ve never been abused or in poverty for example. You could say that I have had quite a easy life thus far. But, I’m not happy. I think about suicide a lot, more than ever in my life. It’s not that my life is so unbearable that I want out, it’s just that I feel completely indifferent towards life. I do not value it at all. I do not have any self preservation left anymore. If I were told tomorrow that I have terminal cancer, it wouldn’t stir up any emotions. In fact I would be glad, the prospect of death would be such a relief. Honestly, if I had access to a easy way out of this life without a family member or friend having to find me, I wouldn’t be alive today.

So, here are the things I want to address if I were to go to counseling:
-I am suicidal.
-I am gay, no one knows, I have no one to talk to about it. This is my biggest concern, I need someone who will understand! It is so hard to live a lie every single day.
-I think I am depressed.
-I have no motivation, my schoolwork is falling by the wayside.
-My mother’s only concern is for her boyfriend.
-I don’t have a relationship with my father.
-I am in love with one of my best friends and it is killing me.
-very low self esteem, which is causing me to gain more weight.
-I have trouble sleeping.
-I asked my mum to sign me up for counseling and she told me that everyone else in the family is “fine” and told me to deal with it on my own. She knows I’m depressed and doesn’t take any action.

So those are the central issues I need help with. I just don’t know what to say to a total stranger. Can you please tell me what to expect? If I feel more prepared it won’t seem so scary. Maybe a little encouragement and support? I need some sort of push to actually walk in and make an appointment, but I’m very scared..