Baby won't sleep! Help!

My daughter is 4 months old and she has never been great with napping. She sleeps maybe 2 or 3 hours during the day if we are lucky. She was colicky so to get any sleep at all now we have to rock her, sing, and turn the vacuum cleaner on. Even then she only sleeps about 20-40 minutes.

When we try to put her to bed, people probably think we're killing her. She kicks and screams and flails her arms (this is with us rocking her). Most of the time we just have to wait until her next bottle. Then as soon as you lay her down, she wakes up.

I've been reading about putting her to bed drowsy so she'll learn to put herself to sleep but she is wide awake as soon as you put her down. I leave her to cry for a bit, but she doesn't ever calm down. I know it's because she's overtired but I don't know what to do to get her to sleep during the day.

I need some help, I do this every single night and I'm exhausted!!! Thank you in advance for any advice!