5 month old not sleeping

[JRTfan]

5.5 month old DD has never been a brilliant sleeper but we were until a month ago down to 1-2 wake ups per night. Now though it's every hour and a half. She will only sleep at night if fed I have tried rocking, bouncing, shushing etc it just doesn't work. She's mainly BF but has a bottle of formula at night, has done since birth I've tried playing with the time she has this and adding more/less bottles it makes no difference. Her day sleep is also terrible even if contact napping or in carrier she will only sleep a max of 30-40 minutes sometimes only once a day. I know this is making a difference to her night sleep but I'm at a complete loss. It's beginning to really affect my relationship with DH aswell as my day to day life and in just constantly shattered. I'm not against sleep training just don't know where to begin or if it would even work on her at this stage. She's a very alert baby and likes to be on the go all the time, gets bored and distracted easily so I can see why she doesn't sleep but I have no idea how I can fix it?! Help!

I went through this with both my DC. I went quite mad and was so depressed from the sleep deprivation, I thought I was going to die and DH was going to divorce me. We had to sleep train. I have no affiliation to this lady but I can recommend her book - Alexis Dubief, Precious Little Sleep. Lots of straightforward strategies on both overnight sleep and naps. It's still a work in progress with my youngest (6 months) but 3-4 hour stretches at night make things more bearable. I wish you luck and hope things improve for you soon.

Thank you @tortiecat solidarity helps and I feel your pain!
I expected the newborn phase to be hard and then we had a nice couple of weeks of 3 hour stretches which were manageable, but now we are 1.5-2 hours max ALL night and a completely random very short day nap situation. I will check out the recommendation there is so much online and I am completely unsure as to how much sleep success is down to temperament and can't be changed and how much we can tweak with some training. I am used to dogs..similar in some ways I guess!
I really dont want to have to spend hours in a dark room or being ruled by nap schedules but we also can't carry on with the current situation.

Yes, 1.5 hourly wakes are not sustainable, it is just soul destroying.
Ahhh yes as soon as you start Googling all of the sleep consultants come out of the woodwork asking for hundreds of pounds!
I agree that some of it must be down to temparament but I believe there are steps that can be taken to improve the situation - both parents and babies need some sleep.

Minimal sitting in a dark room here and we aren't able to be nap schedule slaves either - the youngest has to accompany me to facilitate the eldest's class and party times!
As to dogs, I think toddlers are basically just puppies
Good luck - and things do get better, if my eldest hadn't started sleeping I wouldn't have had another!

@JRTfan
Can I ask if you've had any improvement on your situation? My DD sounds very similar, currently 5.5 months and there's no end in sight!