Huge sympathy, I did all the nights with dd1 and it’s hellish when they have a blocked nose. When you are unwell too (or recently have been) it feels like you just won’t get through it - but you will.
im sure you have tried some of my top tips but here goes…
I did buy a cold-mist humidifier, the dampness helped (for coughs too). Got that up and running in the bedroom all night.
Slightly raise one one of the cot so she isn’t lying flat.
nose-sucking device (ugh, it never really worked for me tbh)
a baby-version if the saline sprays for the nose. I found that better than the nose-sucker
very long bath before bedtime to get sleepy and melt the gunk in her nose
a little bit of Olbas oil in a tissue near the cot
or Co-sleeping could be an option? (look up safe bed sharing). There’s something about being close to mum that helps.
When she couldn’t breathe I used to turn on the shower and let the room get steamy then stand rocking her to sleep in the bathroom. Same for the endless coughing.
Oh and you can try having warming water in a flask by the bed, a little sip will make her feel better in the night?
Last idea - do you have a friend or family member who you could ask to watch the baby so you could get a few hours of daytime sleep.
I wish I knew you, me and teen dd would be right over to your place to help you get a break (and sneak in some cute baby time). Im sure there are lots of people you know who would help - reach out to them.