My camera fell and my 70-300 Tamron lens hit the floor first and after that I can't remove the lens from its body. I think some parts of the lens cracked and it got stuck. How do I fix this? Can I fix it on my own or should I let it be fixed in a camera shop?
Sounds like the lens mount or locking pin got bent... this is not going to be a pretty or cheap fix as the parts are not accessible when the lens is mounted.
Does the lens mount release button push all the way in? If not, you can try twisting the lens back and forth while you push on the button and hope it works it way in to release the lens. Or you could try forcing the lens to straighten the locking pin, except that you don't know which way to bend it and it's not that easy to do. If you can get them apart then you can deal with the aftermath appropriately. If they won't come apart it gets even uglier... either the lens or the body has to be sacrificed (at least a part of it).
I would probably send it out for a repair estimate and hope for the best, but expect the worst.
That sounds like a pretty severely damaged lens (and camera?!). I would suggest to not touch it at all (broken glass might fall out and hurt you) and send it immediately to Tamron's repair centre - if it is still in its 5-year warranty period.
Whatever you do, do not try to repair it yourself: most likely, you will damage the lens even more, and judging by what you said about glass cracking, you might even hurt yourself.
But please bear in mind that, from what you have described, I think that there is little hope for your lens.