You guys do realize that asexual/aromantic people are still perfectly capable of forming deep, meaningful bonds with other people? It's very possible for someone to want to be close to another person WITHOUT any of the usual physical intimacy we associate with our "normal" relationships. I've had a number of friends like that myself.
The only advice I can really give is to look for other asexual people to date. They're not common, but they are out there. Otherwise, if you can just find a best friend who's willing to cuddle sometimes and go places with you, that might be your second-best option. It's nearly the same sort of relationship, except they would be free to be with whoever else they wanted.
I would also suggest that you try to go out and make like-minded friends whenever you can. Simple conversations are where the best relationships start, and for someone like you, it can be easier to find a close friend to fill that void than someone willing to date you on your terms. Again: I'm NOT saying that it'd be impossible for you to find someone perfect for you, there's probably several someones out there who would love you just the way you are, but I AM saying that people like that are really hard to find, and it's not a bad idea to try to patch up the holes in your heart with a few friends until you find that person.