I'm really sorry to hear you're having such a hard time. We've all been there at one point or another, had our hearts broken by someone we deeply cared about. I had a bf stop talking to me/taking my calls once and it was very difficult to take. I guess some people just need to make a clean break in a relationship, and can't deal with all of the closure issues that come with a breakup.
My advice to you is to leave Tom to it. You've done all that you can, calling, e-mailing, and trying to explain your side of things. As much as you want for him to listen, if his mind is made up, there's really nothing you can do. I know that this is difficult to accept, but if he can't even hear you out, is he really worth chasing after?
Don't beat yourself up over the arguments, either -- if things were completely OK between the two of you, you wouldn't have argued like that. And if he can't bounce back from an argument, then that is a sign that perhaps things weren't meant to be. Long distance relationships are hard enough as it is, and I realize that arguments can arise due to communication issues (talking too much/not enough, or meanings being misconstrued when you're IM'ing) but when someone is unforgiving like that, things do just fall apart.
The thing to do now is take care of yourself, and take the time that you need to get past things. Don't listen to your friends -- you can't put a time limit on the healing process. Just do what feels right for you, and when you feel ready to date again, you will. Treat yourself -- go out for dinner, or buy that pair of shoes you've been wanting. Do some things that you've been wanting to do, but haven't found the time for.
Don't sit and second-guess yourself. Be confident in your convictions, and don't feel bad about speaking your opinions, even if they resulted in an argument. Life is too short to hold your feelings in, and worry about what others (even loved ones) will think of you for expressing them.
I know it feels like agony now, but the sadness DOES pass. The best thing for you to do, is just distract yourself with other things so you don't have so much time to think about it. And don't worry about what Tom is up to, or why he won't take your calls. He's the one who's lost out.
Hope you feel better soon! You're not alone here on the forum
~Michelle