Be aware that the approval process is long and slow. Not as bad as SS disability, which can take years. But you should be prepared to support yourself for at least a couple of months while the insurance company drags its feet. I'm currently on long term disability. It took my insurance company 2 full months to approve the short term and 3 months to approve the long term. Between the two, I've had 14 weeks out of the last 6 months where I had no money coming in at all. I will eventually get back pay for all that time, but in the meantime I've drained a lot of my savings. And disability doesn't pay 100% of your salary. Plans vary, but I get 60%. So you also need to be prepared financially to take a pretty steep pay cut.
I'm not saying this to discourage you. If you can't work you need to apply for disability. But you do need to be prepared for the financial impact. Good luck to you.