Hi!
Congrats on your new arrival!
You are all going through a huge period of adjustment ATM so firstly, go easy on yourself.....life with a toddler & newborn can be very tiring (BTDT
!).
Has your DS ever been an independent sleeper or has he always been rocked/fed to sleep?
I would definitely wait until he's feeling better before starting any kind of sleep training + molars can also mess up sleep quite badly (also going through this with DS currently!). Have you tried doing a dream feed of meds in the early hours to help with teething? I've found this has really helped my DS....
Unfortunately, when a LO is prop dependent to fall asleep, there is no quick way to resolve it, but I appreciate with a newborn that's not what you want to hear!
The issue you have is that you are all sleeping in 1 room....I was going to suggest GW (Gradual Withdrawal) but this wouldn't really work in your situation (I guess also your new LO is in with you too?)......will have a think about what else you can do & I'll be back a bit later....