I agree woth everyone else, you are still very much "in the trenches". Sleep WILL come again. What practically can you do to improve your sleep right now? You've identified it (quite rightly I should say) as the crux of your problems right now.
Can you co-sleep? (I did at this stage with my first as he was up an average of 5 times a night and sleep training wasn't working for us)
Have you tried sleep training?
Can you and your partner work something out that prioritises your sleep? I EBF (not by choice, wilful child wouldn't have it any other way!) so I had to do all the feeding at night. He would then get up with our baby in the morning, do breakfast, play with them, get them dressed etc to give me a few hours of aplod sleep before the relentlessness started again, would something like this help you? Any family to take baby for a few hours each week to help you put your head down also? Initially I remember always feeling like I needed to "catch up" on sleep, but after a while I stopped thinking like that and it helped me to cope mentally with it.
Don't even think of adding to your family right now, that's just putting unecessary pressure on yourself and beating yourself down. I remember thinking I am NEVER doing this again, this is SO hard, how do single parents do it, parents of high needs babies etc etc because it IS hard.
The answer is, you wait until it feels manageable again. My about to turn 3 year old SLEEPS through the night, is smart & funny and just a fantastic little dude, this stage renewed my desire to have a 2nd.
Fmdont think about it now as I say, but there's hope for the future I promise ❤️