PPA or exhaustion?

I can’t get enough sleep. Our baby sleeps ~5 hours, then two, then two. But I’m awake nursing him, rocking him to sleep, having trouble falling asleep listening to him. I’m going crazy. I’m spending all my time getting him to nap or trying to fall asleep while he does. I just want to live my life but I’m too exhausted to do anything. I think it’s turning into PPA where I dont want to leave the house and I’m becoming obsessed over googling what’s best for him.

I know he’ll sleep better and I will once he’s in his crib and I’m in our room upstairs. I joined a Facebook sleep group... But I feel like 3 months is too young to cry it out. I’m terrified he’ll feel anxious or abandoned and the reason he’ll stop crying for us is because he know we won’t come.

What do I do? I want my sanity back. I need to sleep. But I can’t stand the thought of my little baby being alone all night crying out for us and us ignoring him.