Major sleep issues 14 week old - please help!

I have a 14 week little girl and we are having terrible sleep issues. 

Bit of background - she was born at term, straightforward birth, exclusively breastfed + gaining weight well, meeting all her milestones but has always been quite an unsettled baby

For roughly a month we have been having these sleep issues - up until then she would happily sleep in our arms for most of the day. She now seems to be fighting sleep massively.

Most nights she has very little sleep. We have a bedtime routine at 8pm of bath/sleep bag on/feed/cuddle. She goes down in our bedroom which is dark in a next to me crib. It can take 2 hours to settle her, we then usually have an initial stretch of 2/3 hours sleep followed by her waking every 30-60 mins for the rest of the night. When she wakes she is very difficult to settle, she is not normally upset but is active and hyper - eyes wide open and farting around, kicking and punching. I won’t always feed her when she wakes, only if she seems hungry which is perhaps twice per night. 

Every now and then she has an amazing night and only wakes once/twice - one night she even slept through so I know she is able to do it but it just seems there is something stopping her the majority of the time. I can’t think of anything that we do different when she sleeps well. 

During the day we are constantly fighting for naps, I have tried everything - sling, pram, rocking/cuddling to sleep, feeding to sleep, the car. It can literally take hours to get her to drift off and often then the nap will only last 20-30 minutes (can be a bit longer if we hold her). I try to take her up for at least one decent nap in the crib upstairs each day and this sometimes helps slightly. 

By the end of the day she looks totally exhausted, and will hysterically cry from around 5/6pm until bedtime. She has red eyes, rubs her eyes, yawns - displays all signs of tiredness but there is nothing we can do to help her or get her to sleep. 

Thank you so much for reading and I would love any advice/suggestions. I don’t want my little girl to be unhappy and me and my husband are stressed and exhausted.