At 11 mos is she eating three solid meals?
Teething, growth spurts all can disrupt what is going on with her sleeping habits. Is she crying hard when she wakes or just kind of wakes up and isn't getting herself back to sleep.
The ear thing could be a build up of fluid, which won't always go away with anti biotics. Laying down can worsen that feeling and it can be painful or uncomfortable. My son had them, it had nothing to do with viral issues, it was the fluid was getting trapped in his ears, he never had signs of infection but irratation and they had to finally put tubes in to resolve the problem. After that there was no problem.
If it is reflux, that can be painful when she is laying down. How is she napping?
If it is teething, try motrin before bedtime or teething tablets.
She at her age shouldn't need to eat in the middle of the night at all. Don't rush to feed her right away. Some kids through growth spurt may but try not to feed her if she wakes, give her at least 10 minutes to try and help teach her to soothe herself.
I never did crying it out until after 6 mos (then rarely did it) and gave it ten minutes to let them settle themselves, they had a fan for white noise and a I got a voice activated sound maching where the music would kick on if they fussed and would wind down after 5 minutes. Those things saved me big time as other then teething issues or growth spurts my kids slept through the night. I just tried different things until I found what helped my kids soothe themselves or sleep better.
My suggestion is figure out if she really crying hard, like she is hurting? Is she just fussing and if you left her alone for a bit give her a chance to fall back to sleep herself.
I wouldn't run in if it wasn't a painful or really upset cry, I would leave her be for a bit. Teaching her to fall back to sleep herself is giving her a gift. If she is in pain, take her back to the Pedatrician and see if you can find out if it is associated with her ears, reflux or may just be teething.
Good luck, it is hard when they should be sleeping through the night and don't! All kids are different.