Poor bunbun. (((Vibes)))
With her tilt I imagine the discharge doesn’t flow away very well. Are you able to clear it a bit for her? I’ve heard you can use an infants nasal aspirator to try suction out the gunk. Taking her into a bathroom after the shower has been used might help loosen things up.
I do agree about going straight onto antibiotic. Being blocked up it would make it harder for her to eat and drink.
Maybe ask if there is anything you can use along with oral antibiotics? Like medicated nose drops. Sometimes eye and ear drops can be used for the nose I think. Also, can be administered via the eye as it goes into the sinus area. I’m not certain if that’s correct for rabbits but I know when I use some eye drops, I can taste them in the back of the throat within minutes.
Was treatment for EC continued after she developed tilt? It can cause tilt but is not the only cause. But treating as precaution was wise in my opinion.
Good luck. I hope you can get her sorted out.
ETA: You might already be familiar with it but this website is all about rabbits with tilt. http://www.onthewonk.com