Once your done making a tab and click submit, does it just stay in your draft section until its approved?
No, it goes to an approval queue... And people will then vote to have it approved and then published...

If you go to the home page and on the lower left side click on TABS AND CORRECTIONS IN QUEUE
You would find your tab in there... Once it receives 5 points in votes then it is published...

If it receives 5 negative points it is then rejected...

What is the name of the song and artist?
If you can't find it on your My Contributions page then the tab didn't go through to the queue. If it didn't go through then there is either something wrong with the tab description (it is shorter than 5 words, contains characters that aren't allowed, etc), or the tab. Make sure that the tab is long enough and that you haven't crossed the red margin line - excess spaces can cause problems if they are too close to the line. You need to fill in the tempo field with a valid number if you have added a strumming pattern.