Poor boy. He sounds desperately unhappy and not at all fit for school at present. If I were you, I would get him signed off school with anxiety for the present, whilst you consider your options. Home education is one of them, but there are other possibilities, which the school may consider if your son is having medical problems, eg. flexible learning (ie. going into school for just a few lessons) or learning at home through the LEA.
"He says he is so self consious that he feels he can't even walk or talk in front of people without strong anxiety. He feels he has nothing to look forward to and feels like no one cares about him. He won't let me hug him".
I agree with exoticfruits that this is the issue here and this is what you need to discuss with the GP.
My eldest son (12) also suffers from anxiety. It's crippling. For quite a long time, like your son, he would stay in his room all day and play 'Minecraft' on the computer. He told me it provided an escape from the stress of his daily life. I was very concerned about his 'addiction' to it, but taking it away completely actually made his stress levels worse. In his case, school was a major exacerbating factor and he ended up refusing to go. He was educated through the LEA for a few months, which is why I mention it earlier, but in his case this didn't suit him and we later deregistered him. However, he is only 12, whereas your son is 15 and approaching GCSEs, so you may need to make a different decision.
I coped with the Minecraft addiction by setting clear limits on computer usage and offering other activities as much as possible. Most of these were rejected and, for a long time, my son would rather sit and stare into space than read, go out for a walk or talk. However, things are improving. Walking a neighbour's dog proved to be a great distraction from the computer and has had nothing less than a miraculous effect on my son (providing him with company, affection and exercise on a daily basis). He is finally getting the colour back in his cheeks.
If I were you, my first step would be to visit the GP and ask him/her to sign your son off school for stress (our GP did this for my son for several months). Ask for a referral to CAMHS as they are the gateway to counselling and medication, if this is necessary. I take julienoshoes's point about not medicalising your child, but there are times when we all need modern medicine. This is down to your judgement, of course, but in my son's case he was so anxious that normal life was impossible for him without medication and I felt it would have been cruel to have refused it (when I say normal life, I mean that he was unable to leave his room or see anyone apart from family for several months and was in a constant state of heightened anxiety and OCD behaviour, which was agony to witness).
I think colleger's suggestion of taking your son's computers, phone games, etc away would actually be very dangerous for your son at the moment and I wouldn't suggest you do that at all. I have forced my son to go 'cold turkey' in the past and would not do it again. Now I insist on moderation when he uses the computer and I continue to encourage other activities, as julienoshoes describes she did with her son, but I don't remove the computer completely.
More than anything, at the moment, your son needs to know you are on his side. You don't want him to feel you are against him. He may not show any appreciation for your kindness and concern towards him - he probably isn't capable of this because he is so wrapped up in his own issues, poor boy - but it is the best thing you can do for him and he will appreciate it one day.
You don't mention friends. Does your son have at least one friend that he sees? This can make all the difference.
Let us know how you get on. Having been through all this with my son, I do feel for you.