I agree that just after graduation is a tough time for almost everyone, because you've been pushing towards a highly specific goal, and suddenly that's behind you, and you are thrust out of the familiar university environment and people, with concrete hoops you need to jump through at regular intervals - suddenly the world is your oyster, but it can feel isolating and disorienting. You're absolutely not alone in this, and a lot of new graduates these days are in your position, living with a parent for financial reasons, which I imagine causes its own issues.
I agree with others who say stop looking around you and panicking because you feel isolated or directionless compared to others - concentrate on yourself, on deciding on the kind of life you want, and the steps you need to take to get it. As others have said, you currently have the luxury of only having your own wishes to consult, and this is in fact a fabulous boon, though it might be only later on in your life that you recognise that.
I always find that a useful tool at what feels like a bad moment in your life is to imagine a time in the near future when all your anxieties are resolved - in your case, maybe imagine yourself years down the road in a demanding career, perhaps juggling children and a marriage and a crazy commute and house repairs, and barely having time to brush your hair, far less return social phone calls. (Or imagine some other scenario that suits your sense of what you would like your life to be. obviously.) What will you wish then that you had done with this time where you have time to concentrate on yourself, figure out your own goals etc?
And don't flagellate yourself for having lost touch with your university friends - and I don't agree with other posters that your distance from them now means they weren't 'true friends'. Truly, I think lifelong friendships come along for most people as frequently as unicorns - that friendships are time-specific doesn't make them any less real. You may reconnect with these people, or you may not, but don't dismiss them as being delusions on your part. There will be other friendships in your future.
Best wishes, and try to calm down about it all. You have everything going for you.