What breed of dog is he? (show us a pic OP!)
It's bloody hard OP. I've got a 6 month old pup and he is hard work at the best of times but is unwell with a cone (that he hates) on at the moment with a urine infection and needs constant supervision. I have a chronic illness which of course is particularly bad at the moment as luck would have it. Obviously I adore him and will do what needs to be done but that absolutely doesn't mean it isn't ok to be at the end of your tether or cry in frustration. When you are struggling to cope with the situation I think its very normal to imagine 'giving up' the dog. That doesn't mean you will or that you really want to, it just means you can't cope with the situation as it is.
How old is your DS? can he occupy the puppy with appropriate playtime until it's sleepy while you sit down, have a tea and take some painkillers. Pup should be sleeping the majority of the day at that age and if it isn't then I'd really recommend enforcing naps (much easier if you crate train), or restricting the areas of the house the pup is allowed in - stair gates, a pen, whatever works in your home. When ours was little I found the worst of his behaviour stemmed from him being overtired. It would also prevent him from being able to mess all over the home.
In terms of eating his poo, I would ensure he is getting enough protein in his diet. Puppies need high protein diets to effectively grow and some dog foods are full of rubbish, which can lead to puppies 'looking' for other sources of protein, eg their poo. Pick it up straight away in the house.
Take him outside any time he has had a drink, and immediately after eating or playing as well as as soon as he wakes up from any nap and start to introduce a toilet command, lots of praise with a high value reward (chicken, or something he loves) when he goes. They can't hold their bowel or bladder for long until they're much older which isn't within their control. Absolutely vital to get an enzyme based cleaner specifically for pet urine for the cleaning. The Dr Beckmanns one is brilliant and only a few pounds. If this isn't done the dogs will return to the same spots to toilet time and time again.
Don't forget yourself here OP, if the pain relief you have for your hand isn't working then get on to the GP for something that does. It will all pass eventually. Try to find time to enjoy him and appreciate how cute he is in an intentional way. If it all feels negative the cumulative effect is much worse.