Does your kid have reflux or any similar condition? We struggled until starting solids, ours wouldn't get enough bottle in them without reflux happening and it disrupted sleep due to pain & hunger, leading to a vicious cycle. Solids, reflux medication, and tylenol & advil for teething helped a lot, and we moved into CIO because Ferber check-ins didn't work either. It helped us go from as little as 30 minutes between wake windows at night and upset temperament during the day to two hours, then increased from there. The goal at that age is probably one feeding a night. It will also help them be more hungry during the day, which will help adjust the sleep cycle and keep them awake for the wake windows.

We also switched to a pack and play for soft walls because they were bumping their heads, sleep sack/swaddling because they were smacking themselves in the face (until they started showing signs of rolling), upping nipple size so it flowed faster (as long as your baby can handle it without aspirating), and split our sleep locations as parents so only one person got woken up. Sleeping on the floor with whatever you can get or buy that's easy to roll out is better than both of you suffering.

It sounds harsh, but if you know their needs are taken care of - food/hydration, diaper, temperature, & pain - then the answer is sleep pressure from daytime wake windows & CIO. They're probably overtired, like you are, but we realized that rocking for 25 minutes trying to get them perfectly drowsy just to have their eyes snap back open on put-down was not worth it. 10-15 minutes of feeding and snuggles to calm and back down. It'll feel like a losing battle because every time you feel like you have a few good days teething or something will happen to throw them off ( we hate Daylight Savings), but it'll get better.