My 11 1/2 week old DD screams before every nap but also does better at night. For her, we finally decided it was her blowing off steam and we now have a routine of going into room, swaddling (we do this a bit differently too as she doesn't like arms swaddled) and sitting still in chair. We hold her cradle style as the over the shoulder got too dangerous with the screaming/flailing and we couldn't pat without worrying about her head falling backward, etc. Anyway, we have done this now for weeks with simple "It's o.k., we're just going to sleep", etc. I don't even pat her back anymore. I think she needs us to just sit still while she wiggles and screams. When she is done, she is still in our arms and we put her in her crib-she is progressing more toward being put in the crib while fully awake as she gets older-she has a hard time settling herself. She does better at night. It has been said (this site and otherwise) that under three months, they organize their night sleep and over three months, they work on their day sleep. This seems true with my DD.
Also, if she likes sleeping sitting up (in swing) and cries (screams) a lot, she may have reflux like my DD. There are other signs to check on site and can ask Dr. We got her on prevacid and now she only cries before bedtime (this is how we were able to notice the pattern once all the other crying all but stopped unless overtired). This by the way is slowly getting better as she is just starting to be able to self-soothe with fingers (would never take the paci).
My DD's activity time is cut off at 1 hour after awake/eating time and then we start her wind down which take about 1/2 hour-10 minutes to settle then 20 minutes in the crib with my hand on her chest or patting her. I don't shh anymore. I think I got sick of hearing myself do it and I stopped and she didn't seem to care. I think all that noise and aggressive patting was too much stimulation for her and she couldn't settle until we stopped all the action and just held her. It's hard to watch her cry, but now that I know what will happen otherwise, I feel more confident.
Hope this helps. Hang in there. I'm told it will get much better in the next month once we work out these kinks. Keep at it.