Write down the different parts you have to do (I don't know which course - but reread material/take notes/essay plan/essay or part a/b/c) and estimate times. Work on a little bit each day rather than panicking about the "whole".
Don't let it get to the last day if you're likely not to hand in. Is it likely you can do it? If its not can you email the tutor and explain (briefly) your circumstance, say you're half way through (or however far you actually get) and that although you're expecting to finish it you might not make the deadline would you be eligible for an extension. But you need not to leave that to the last minute.
Honestly the best thing is to carve out an hour or two here an there, stop panicking about the "big picture" and just crack on with getting a bit done. All the little bits add up. Make sure you do a bit each day or each time you get a chance.
Talk yourself back down out of a panic
"it's going to be shit" "well it might be, but a completed essay will be better than no essay so I'm going to stop worrying about it right now and get on with it for an hour then have another think."
Its kind of mental games to play to help you just get on with getting something done. Once you're in the flow it might get easier and worse case scenario is you hand in something that passes rather than distinction but at least you have something to hand in!
I take my hat off to you. I've recently just sat some exams (I'd failed twice before) and I completely underestimated how difficult it would be revising with a two year old. And i was fortunate that I had a DH who came home on weekends.
When I was doing essays I would do rough drafts and progressively bulk it out with evidence to back up my argument. So I'd start out with a sheet just with just the main point written down and then a sort of flow diagram showing my train of thought (for, against, dissenting views, etc) so that the essay would flow.
I did a number of courses with the OU and I remember the EMA panic. There's some good advice upthread, I would just add something that helped me. I find I work best in short bursts, so I set a time for 25 minutes, have a 10 minute break and then do another 25 minutes.
Stop thinking about the time left! You've got all evening to get a first draft done so you will be fine, instead keep reminding yourself of what you've just said, the plan is the hardest bit and its easier now.
You can do it. Keep countering the negative thoughts and then just sit down and crack on with it this evening.
I had to fight the negative self talk right until the end!!
I've restarted smoking though...DP's gran died last week which has added some extra pressure (we don't live together atm for money reasons but i've been supporting him a lot this week & it has been stressful in itself, for both of us). I almost quit and was down to 1 a day, in the evening.
Sounds bad but it's helped with the stress of this week to not also be trying to quit smoking. I'm sure i'll conquer it when I've not got so much going on and DS is 20 and has moved out