I remember that stage with our sleep-fighting little demon :-) I tried everything to get her to sleep. This is what I found worked:
If she falls asleep while feeding let her sleep as sleep begets sleep. The more she sleeps earlier on the day the more she'll nap later on and then at night. It's absolutely true.
Try to get her to sleep about 1-2 hours after she first wakes up. DD was dead easy to get to sleep at this time and it REALLY helps with naps later on.
DD would only fall asleep on us (still only does at 7 months) by rocking her and patting her back at the same time to mimic the movement in the womb and heartbeat.
Shhhing really helps and using a swaddling blanket from amazon so she can't get out. Both again mimic the womb.
Walking in the pram or driving in the car sometimes helped. Also walking around the house with her in a baby carrier was an excellent way of getting her to sleep. We did that loads before she was 3 months.
You have been using a dummy? I am firmly in the 'gods gift' camp regarding dummies.
We thought that DD had colic due to crying/screaming in the evenings. While she was on her back, holding her legs in the air and circling to release any trapped wind seemed to work. Although looking back I think it was over-tiredness.
After 3/4 months it all died down and now for some silly reason (because she needed us so much?), I kind of miss all that. Maybe I am getting nostalgic for when everything was so new and exciting/nervy with the oxytocin and adrenline in combination. Or because it felt so special with a newborn and that won't ever happen again. Sorry getting silly now.
It will get better for all of you :-)
But if it doesn't get better go to the health visitor/baby nurse/doctor and really badger them about reflux or possible cows milk/lactose intolerance. I have friends' of friends whose babies screamed loads and they were always palmed off with 'babies always cry' for months! I think the opposite - that babies cry for a reason, but most of the time it is either solvable or managable, if it isn't there is something that needs to be investigated.