really feel for you as had similar experience. ds was pretty high maintenance (spirited I called it), still is now at 17mo but in a different way, and cried a lot and wanted held all the time -I just had to let go of all the housey stuff and focus on ds - once I decided to do that I felt more relaxed - funnily ds seemed to calm down a bit also.
Would take him into bathroom in his bouncey chair while I had (long!)shower. even if he cried I kept in my mind that he knew I was there, could see me, he was safe etc. Would sing to him from the shower too!
If your ds still cries even if you hold him I would put him down and let him cry for a short while and see if he settles a bit, to see if doing something different works.
ds liked a good cry (read - screech!) before sleeping - almost as if he was letting off steam, and I found that lifting him up would sometimes aggravate him when he was really tired and just wanted to settle himself sleep. I just let him do this for a few minutes (and hover nearby) and he would just calm down and go to sleep. Know not everyone goes for this but I found a dummy also helped ds calm down.
Would say your ds is too young for cc as yet .
ds also diagnosed with reflux at 12 weeks - was screamimg after feeding - get GP tp check this out just in case, maybe also has colic, which I think reaches a peak about this age?
It took me until ds was 4 months before I started to work him out and could relax a bit - like realising he wanted fed every 3 hours, not four, when he was tired etc and then he cried much less, and I was more able to work out why he was crying when he did iykwim. Once this happened I gradually got some time to myself / housework done.
Give yourself time to adjust, anything over and above looking after ds and yourself is not essential.
Even if he screams in the buggy you might find it easier to cope with out walking instead of feeling cooped up in the house with him.
It does get easier, honestly. Once he learns how to settle himself / let himself go to sleep and gets into his own routine of sleeping / feeding you will get some of "me time" back. But he's still a tiny baby just now who doesn't know how much you valued that!
Hope things get better soon