I think the problem is that you are not doing anything to help her feel comforted and relaxed to get to sleep.
You use white noise. But white noise in itself isn't a comfort for getting baby to sleep. It's purpose is to drown out background noise to help a light sleeper to not be woken easily.
And stroking her nose evidently isn't actually helping, since she still screams for a long time before going to sleep. So it's more or less ineffective.
You seem to have completely discounted the two basic sources of independant sleep comfort - movement and dummy. I'm dubious as to why, since what you are doing is definitely no better and is teaching nothing.
The current way of things is that baby screams until exhausted, drops into a restful sleep when she simply cannot stay awake any longer and then wakes easily because the sleep is not restful. Thus perpetuating the cycle of baby being sleep deprived and exhausted.
So if you have discounted the tools of independant sleep, your only realistic alternates are to embrace attachment parenting - cosleeping, feeding to sleep and naps in your arms.
You need to find ways to actively help baby learn to be calm and relax. Just lying baby down and hoping that she will 'just learn' is unlikely to happen. She's going to need you to be proactive about it.
With a toddler, a bouncy chair on tge living room for naps will be your friend. And a dummy, I would suggest. Follow a simple cycle of
(make a mental note of the time)
(offer a bigger bottle than baby will drink)
(Watch the clock, stop after 1h from waking)
(Offer what is left in the bottle)
(Into bouncy chair with dummy, chair in front of you as you sit on sofa, feet on bouncer frame, gentle rhythmic bouncing. Relentlessly until asleep)
Wake and repeat over and over and over again.