i really want to reply to empathise. My 15 week old bub is very similar I had hired a hammock and would sit and rock/bounce her to sleep all day to try and get 45 minute naps. I sat there and she would wake between 5 -20 mins later and i would bounce again to get her back to sleep. Very tiring, i couldn't go anywhere. She was so overtired and grumpy and I just wanted to be able to enojy my baby.
Then I went to sleep school for a week and learnt so much about sleep. I also learnt a great way to teach her to self settle... now it does involved her making noise, but there is no timing and she never get's distressed.
Try it if you're comfortable, Make sure bub has a clean nappy, full tummy, has had some fun awake time, is tired enough to sleep and whatever else you use ie comforter dummy etc. (My baby won't take anything and hates being wrapped too). Lay bub down awake and tell her it's sleep time, give her a cuddle and walk out. now listen... If she's quiet leave her, if she's grizzling leave her, if she sounds distressed go back in and reassure her, calm her anyway you feel you need to ie pat on bum, shhhing, cheek to cheek etc avoid picking up but if you have to that's fine. When she's settled leave again (remember it's not about timing). Continue to do this up to half an hour, always get bub calm but not asleep. If after half an hour she's still not asleep help her a bit more, stay in a bit longer until she's asleep. You can just try again next time.
Distressed is continuous crying that makes you want to go get bub. if it rises and falls back down to a grizzle leave the baby they are still in control. GO in if you feel they are getting out of control and need you to reorganise their feelings.
Lily went from wrapped, breastfed to sleep then waking up as she was put in her hammock and bounced for about an hour to... falling asleep on her own in a cot unwrapped with 0 - 5 minutes grizzling by the end of the week.
I really like this method as i absolutely can't stand to let her cry, but I was able to let her learn to settle herself. No tears, no stupid timing, no rules about what you can and can't do, you're just listening to your baby and allowing them the opportunity to learn. Subsequently she now resettle herself at night and i get up to 6 hours when until 13 weeks she woke every 20 -45 mins around the clock.
She still catnaps but we're working on that and she is much happier. Teaching your baby to self settle painlessly is in my opinion such a wonderful gift

I hope this is useful