At this age roughly, I kept mine awake for about 90 minutes to 2 hours a time until the sleep signs, such as rubbing nose, or eyes or yawning. Then I'd take them into a darkened room and settle for a sleep. It won't be long and they'll probably prefer napping at 10.30am and 3pm but not yet.
There comes a point where they become much more aware of their surroundings and may resist naps. However it is absolutely essential that they learn to nap, as otherwise it becomes a vicious circle whereby they're so overtired that they cannot settle easily as a stress hormone is released when overtired. Learnt this from this book.
Seems to me that co sleeping isn't helping her sleep better, as otherwise I'd say just do that for now. If no one is getting any sleep then you might as well do something useful and help her to learn to sleep. I don't really like controlled crying but the method I read about in the baby whisperer has worked for both of my children. If you know they are tired, they have a clean nappy and have recently been fed, push on through with getting to sleep. Maybe try some teething gel too? My 2 kids started teething by 4 months.
Just pick them up until they stop crying and then when they stop lie them down, when they start crying again, pick them, when they stop, lie them down. Do not leave the room with them, stay by the cot and keep doing it over and over. They will get the message in the end and finally go to sleep. It'll take 3 days of being consistent. The first time you may need to pick them up 70 times, the next nap time maybe 50 times etc. This is the method I used. I didn't feel so bad, as I wasn't leaving them to cry it out alone It does work. I think this did come from one of the baby whisperer books originally. As I said if they fed, clean nappy etc and you know they're tired, push on through.
It does require patience but it is worth it in the end. I don't really think you have another choice here though, as things aren't going to get better otherwise. As long as she isn't poorly or anything like that, I think you may have to bite the bullet here. Start with the daytime naps and as she masters those, then move onto the night time, whereby you only offer cool boiled water unless it's the bedtime feed, the 11pm feed or 2 or 3am ish they wake for. Does that make sense? So start with daytime naps first, you can't do it all at once. Too stressful.
But if my advice makes you feel uncomfortable, just disregard it.
Eitherway I hope things gets better soon.