just can't cope anymore

[incensed]

My 13 mo DS has never slept for more than 4 hours day or night. That means neither have I for over a year. He is still breastfed and I feed him to sleep. I am just so tired with a three year old DD to look after as well.
Yesterday I decided I just can't go on like this. He will only nap in the day if he is in the car and then only for 20 minute periods. I am sick of feeling like I am wading through mud, waking every morning feeling groggy and dreading the day, forgetting things, snapping at my 3 year old and generally feeling shit.
All day he just wants to be carried around because he is so tired, he howls if I put him down and I have to do everything one-handed.
Today he was up at 6am as usual, he had not napped by 2pm and was wailing with tiredness so I just put him in his cot and stroked him. As soon as I got up he was screaming and he didn't stop for two hours during which time I went up between 30-40 times to lay him down again , stroke him and leave the room. He eventually sobbed himself to sleep for 25 minutes and now it has just started all over again.
He has multiple allergies (inc dairy and soya) so stopping breastfeeding is not an option. I know it is my fault he cannot settle himself to sleep and it is a bit late to start now but I am absolutely at the end of my tether and feeling desperate.Any advice gratefully received, thanks.

I was about to suggest there might be some reflux issues, and then saw the allergies, assuming you are super strict in what you eat? Have you looked at gluten as a possible source of distress?
There's also a lot to be said for paracetamol/ibuprofen when they're teething imo.

DD is pretty much the same actually, but it's no worse than DS was so I'm not expecting much more if you see what I mean? I managed my expectations of the sleep I would be getting for 12-18 months. I'm knackered and am looking forward to her sleeping through. This will happen eventually.

Oof that is rough - but I don't think it is your fault.

Have you looked at the No Cry Sleep Solution?

It's not too late to teach self-settling and to me it sounds as though that would be the way for everyone to get more sleep and for your ds to be more contented while awake. I'm sure many will disagree with me but I really don't get the argument that sleep training is cruel- surely it's a bit harsh on a toddler or baby to be expected to function on little sleep too!
I would suggeat reading up on some sleep training methods and stick with one. Personally I would recommend the Baby Whisperer. I don't think any sleep training is easy and you have to expect ups and downs but stick with it and feel confident that it will work. Generally speaking, gentler methods take a bit longer. A lot depends on your child's personality too. I did Baby whisperer pick up put down but in hindsight suspect that dd just wanted to be left alone to go to sleep as she seems to do fine on her own.
Good luck xx