I know this is a very hard time for you, I was defined by my career and felt like I lost my identity when I could no longer work.
You WILL get past this, you WILL adjust - just hang in there - you are not a failure... you just have been given a different kind of challenge than what you expected.

Now about SSDI (I have no knowledge of state)...
one important thing - do NOT move down to part time work before stopping work.
The decrease in pay will hurt you forever - SSDI is based on your income over a certain number of years, if you decrease your income you will get less.

You have to be unemployed due to disability for 6 months to qualify, and you have to be expected to never be able to work again. Apply as soon as you qualify - it is a long process.

Don't be surprised if they deny you at first, sometimes they deny vrey ill people - just appeal. Don't give up.

DO as much research as possible before filling out the paperwork, and try to get a trusted person to help you if you need it. The paperwork is difficult to deal with when you're feeling bad.

Don't hire a lawyer unless your appeal is denied - they take a pretty big chunk for their fee - having said that, they could be the key to getting approved.

Best of luck to you - hang in there!

Note:
If anything I've said here is out-dated, someone please correct me, it's been over 10 years since I did this.