Maybe the belts are out of sync by 1 tooth. I had that issue from the factory and it took me a while to figure that out. I kept trying to adjust the tension and it wasn't helping. I had to loosen both belts completely, move the carriage to the back of the printer, make sure both belts were in sync, and then tension the belts.

As long as it works, good for you.  The proper way to align the two Y belts would be...

This can be done with the motor drive belt installed but you may find it easier with it off.
1.  Loosen the set screw on right rear drive pulley and ensure it is loose on the drive rod.
2. With both hands (one on each side) move the gantry front to back and back to front a few times stopping in the center.
    The tricky part is stopping where the right side feels as though it is sitting in a neutral position.
3. Tighten the set screw without rotating the drive rod or moving the gantry.
4. If you chose to remove the drive belt reinstall and be sure it is snug but not over tight.  If it is too tight it will cause   
    binding of the rear drive rod.  You'd be better with it too loose and tighten some if backlash is a problem.

I had to loosen both belts completely, move the carriage to the back of the printer, make sure both belts were in sync, and then tension the belts.

+1 for this. I had the exact same issue. My belts were off synch. Loosen the belt tension on both, re calibrate as standard, and then tighten. 
And then in my case, loosen again, as I over tightened.

Any ideas what is going wrong?

You got solidoodle'd.  What printer is it?  Many of us have had Y axis binding issues on various solidoodle machines.  Best case is you just realign everything and it works for a limited time.  Worst case, you end up rebuilding the entire axis from new parts that are actually quality.  That's what I did.  A good place to start if you have already aligned your carriages is to take your calipers and measure your Y rods in several places and note the diameters.  They should be 8.00 mm.  If these are out of tolerance, there is not much you can do that will make a long term difference. 

If you do end up needing to replace the rods, go ahead and do the Lawsy carriage mod at the same time.  Y direct drive is another mod that is highly recommended.  Hit up the search function for a lot more info and let us know if you have any specific questions.

I can get the Y axis to work momentarily via the motor but then it quickly jams again from the right side as far as I can tell (on the opposite side to the motor) so I think the problem is here. Then when i try to move it by hand I can't and the only way to free it up is to loosen the Y axis motor/belt. I've spent time greasing the bearings and adjusting the belts but the sweet spot seems very difficult to find. Any ideas what is going wrong?