5 month old won't sleep at night - help!

[Mariesusu]

Hi everyone,

First time back since my DD is born but things are getting desperate in my household!
She is 5 months old and on a good nighttime and nap routine. She falls asleep on her own at night and for naps I put her down drowsy and shush-tap her a little untill she falls asleep. She has only ever napped for 30 minutes in her crib. She sleeps better in the car seat, stroller or with me in my bed! (That's the only way I can recuperate from my horrible nights)

Her nightwakings have become horrible, waking every 10-20 minutes or at the most 1h30
Here was her day yesterday;

5h00 Feed & tried to put her back down by shushing, placing my hand on her
6h30 up
7h00 Tiny bit of cereal and pear
8h15 S
8h45 A
9h00 E
10h30 S (in the car seat)
12h00 A
12h30 E
1h45 S
2h00 - 3h00 3x 10 minute power naps
3h30 E
5h30 - 6h30 S (had to wake her)
7h00 E
7h30 S
9h00 - NW - pacifier
9h45 - NW - bottle
00h15 NW - fed
1h30 - 3h00 woke up every 10-20 minutes. Pacifier would fall out, she would wake up 5 mins after, so eventually I would take it out before she fell asleep, would only last 10 minutes longer before she fell asleep again. I would pat her gently, place my hand on her...tried feeding, wasn't hungry
4h30 - 6h00 NW Tried feeding, not hungry, did same as above
6h00 - fed

This has been going on and off for a month
I have to mention that I have gotten in the bad habit of taking her in the bed with me so we would get a decent amount of sleep. Otherwise she sleeps in her bassinet beside the bed. At this point she is outgrowing it and I would like her to transition to her crib, which in the same room as my 20 mo.

Any thoughts on what I can do to help her transition her sleep?  Is it a prop problem ?(paci & my bed)

I'm at a loss - any advice would help, thanks!

[Martini~]

Is she having 4 naps a day honey?

[Mariesusu]

Yes. She currently has 4 x 30 minute naps a day. Sometimes we get a good nap in the afternoon (1hr - usually in the stroller/car seat or in my bed) but other than that they are 30 mins.

[Martini~]

Yes... Her A times seem to be extremly short for her age. Is that a reason for that? Even for the first nap you put her down after 1:45A time when at that age it could probably be more 2:15-2:30. That could be a reason for short napping.

Have you seen a sticky with average A times in our FAQ?

[Mariesusu]

Yes, I've been trying to push her A times to over 2hrs. Sometimes she's just too cranky and falls asleep as soon as I put her down...usually at the 2hr mark. Then again, we get short naps.
This morning was good, we got 2h30 A time and 1h15 nap.
What could explain her waking up every hour at night? Is it the short naps?
I'm also staring to top off her breastfeeding with formula as it might be that she's not getting enough milk from me.