I have had two little boys (one with ASD - mild) now in their teens and preteens and they both were desperate to get "out" every day. I think toddlers get extremely frustrated stuck at home, even surrounded by toys. Any outing will do, shops, playgroup, park. But they have to get out and be moderately active or have a change of scene. So don't feel your son is unusual in this, even though he is still only a baby/toddler.
Secondly sleep really is the key. You are exhausted and so is he. It is affecting both of you. That is the first thing you need to see a HV/GP about. My ASD son had a lot of trouble self settling in comparison to my other two children, so that could be an aspect, but it is something you can encourage - good sleep patterns I mean. He may be naturally bad at sleeping and someone needs to support you in helping him get the sleep he deserves.
Also food. Toddlers are terrible fussers with food. They pick on stress, they get defiant, they are frightened of being made to eat things they don't fancy. They also get hungry very quickly. The combination of not eating and needing to eat is a lethal one. So it helps to have lots of easy snacks that you know he will like rather than kill yourself preparing food he throws on the floor. Maybe apple slices, cheese sandwiches (babybels even?) a few crisps (just a few, in a little sandwich bag - not a full branded packet he can recognise) humous and things he can dip in it, little meatballs or chipolata sausages. Food he can eat out and about so you can defuse the bad meal time atmosphere. Have a picnic on a park bench.
Yet this is also a ASD issue. ASD children are notoriously sensitive to taste and texture, and will refuse to even taste something that they are suspicious of, even when hungry. They just hungrier and more badtempered as a result and even more impossible to handle. SO give him some slack if you suspect he has food "sensitivities". Give him food you know he likes - it can still be healthy, even if it is repetitive and quite limited. It's a start.
Toys. Toddlers are much more interested in gross motor play (well in my experience of boys). Jumping - sliding - fiddling - banging - whooshing. They like songs, marching bouncing, wrestling play. ASD children also need a lot of extra sensory input which means they need to touch things, grab things, squash things, bang into them. Which would account for why he won't leave you alone. But often babies toddlers pick up on depression withdrawal anger and want to interact more with you, in a negative way, which is what he doing perhaps?
Boundaries. Timeout and smacking don't work for toddlers. Distraction and routines do. Empathy and shared fun works too - that sounds a bit facile but when you both feel happy it is much easier to behave.
You. This sort of stuff would make anyone overwhelmed and depressed so it is a bit of a chicken and egg to blame his behaviour on your depression. The two go together. You are his mum and if you are unhappy he'll feel it in his bones and that will stress him too. So you need to get someone to listen, and give you some strategies to make both your lives easier.
So, having lived with three toddlers, one with undiagnosed ASD, I so sympathise with feeling unable to cope, but when I DID cope it was because I accepted some of the stuff I've listed above. Looking back I think mothers get very confused about how their toddlers should be behaving and sometimes don't accept them for what they are, toddlers.