I was the same way. Every cartridge razor I tried irritated my face. I learned shaving with williams soap and a Walmart brush. I tried canned goo which just made it worse so back to williams. Yes my 9 years in service having to shave every day was fun.
Then 13 years ago I decided to try a straight razor just for the bad ass effect and found this site (then called straight razor place). I learned actual proper lather, proper prep how to use a straight, proper aftershave and better soaps and creams.
A few years ago I started also using safety razors, although I can get close to straight razor shave with one of safety razors it isn't quite there.
Now I fluctuate between straight and safety, guess what no more irritation.
My advice would be to learn safety razor (unless you want to go straight to straight, full pun intended). Get a good brush and soap/cream and jump into the wetshaver rabbit hole. I recommend safety because though it has a learning curve the curve isn't much.