9 month old not sleeping day or night

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My 9 month old is hardly sleeping at all. He didn't nap at all yesterday and has been awake since 2am. I cannot cope with this level of exhaustion anymore and feel sick with tiredness. I also have a 3 year old and I am finding I am snappy and miserable with them.
What can I do to get my lo to sleep? I am desperate.

Are they walking? Crawling fo they get tired from going to groups etc?
Teething?
I found my 22m still needs to have first nap after about 3 hours of waking

Ensure he gets lots of fresh air during the day and plenty of time to crawl/cruise
Ensure he is getting enough food and drink so he is not thirsty or hungry going to bed. It could be a growth spurt.

If the above doesn't produce the result you need, then try sleep training. It isn't popular on here but you cant have a 9 month old not sleeping and it may be your last resort

Good luck

Was your 9 month old previously sleeping better? There is a sleep regression at 9 months, as they learn social referencing and can remember that you still exist when they can't see you, which gives them separation anxiety. It's actually progress, although that probably isn't much consolation. Most babies have a bit of trouble around this time, but some are worse than others. I thought I was genuinely going to have breakdown from sleep deprivation. It was unspeakably awful.

The bad news is that sleep training at this stage is really painful, and doesn't work very well. We tried it anyway in desperation and her sleep did improve enough to keep me sane (waking every couple of hours instead of 45mins) but it wasn't fun.

The good news is that it gets better spontaneously a about 11 months as they come out of this phase. At that point sleep training works SO much better. It was like magic.

There's a book called 'bed timing' which explains how development stages affect sleep training. It doesn't tell you how to do it though - I'd recommend the Millpond book for that (the kindle version isn't expensive)

What have you tried to get them off to sleep for a nap? If all else fails I out mine in a sling and smart walking - she caves eventually. If no sling then a buggy.

It's true about it spontaneously getting better at 11m. DS2 was an awful sleeper, and I mean that from the day he was born until about four weeks ago (he's just 1) he never napped for more than 35 minutes and never slept for longer than an hour at a time at night. But at about 10.5-11m he just suddenly started dropping night feeds by himself and now wakes up only 2-3 times a night and goes to sleep with just a cuddle, not a feed. He naps for an hour or so at lunchtime (still only 40m in the morning but that's fine). We didn't do any form of sleep training at all, we didn't change anything, he did it all himself.