Well, if you're just joking around...by all means, get drunk and stay drunk. And if you're just wallowing in the immediate aftermath, go ahead and indulge yourself for a few days.
BUT...
If you're serious about "what should I do" and it's been more than a week...you should figure out why you got dumped. Because honestly, nobody gets dumped "for no good reason". Whether you consider it a good reason or not, she had something that she considered a good reason. Find out what it was...that's step one. Step two is to figure out if the reason is something that just lost you your ex (and is unlikely to effect future relationships) or if it's some issue that is going to keep coming up and screwing you. If it's the latter, then step three is to work on whatever that problem is, to try to improve it.
Staying drunk is just a sad way of avoiding your problems. And you'll never really move ahead in life if all you do is dodge the issues you have...you have to face them at some point.
And there is one final point...if you get drunk/stay drunk, all you'll be doing is justifying your ex's actions (i.e. dumping you). Do you want to give her the satisfaction? I didn't think so.
PS-
We've all got problems, some of them serious enough to have to work on. That doesn't make you weak or bad...just human. But be a big enough person to try to work through 'em.
