Congrats D.!!! My first son had a difficult birth too, his apgar was really low initially too (2/8), and he had to spend 4 days in the NICU. He was also really "colicky". In the grand scheme of things I think b/c he was about 3wks early it was just such an adjustment for him to be in this world. But in addition turns out I had some breasfeeding issues. I had an hindmilk/foremilk imbalance and he also was sensitive to dairy & wheat. But once I cleared that up he was such a different baby. I also think he had a mild case of reflux, but that resolved @ about 3 months. I don't know if your bottle feeding or nursing, but you might want to look into that as a culprit..
Now my 12 week old son sounds just like your daughter. He has been so much harder than my first. I might also have a imbalance again, but even w/ fixing that he is just irritable all day long. And from 3-8pm he screams non stop and nothing can console him. Now I guess my 1st could have been that bad but he at least took a binky & that would calm him down. Not my 2nd.
So oddly the only thing that calms him down is, taking him into the bathroom and turning on the shower and laying him on the changing table...I've spent many hours in the bathroom. The only thing I can think of is that's where I use to de-stress while pregnant & its comforting to him.
I've also realized that you are correct in the being tired thing. He gets really colicky when his brother hasn't allowed him to nap or if he gets woken up from a nap when he wasn't ready; sometimes my 1st wakes him, other times its his tummy, or the hiccups and he just gets plain MAD....And then it just cycles like that all day long...
BUT the good news out of all of this is that THIS week (keep my fingers cross) it seems to have all disappeared. SUCH a different baby. I haven't done anything different at all, only difference is he's sleeping better & not waking up at every little thing.
Rest assure it does pass, and since your lil' one had a rough start it may take little longer to adjust. But my last suggestion is to go in a room where its pitch dark, make sure its dead quiet and just hold her and comfort her as much as you can. Swaddling worked until last month for my son, now it just gets him even more MAD. But I basically hold him really tightly, so his arms & legs stop flailing and bounce him until he goes to sleep. Sometimes they just get so overstimulated, and upset that they can't calm down that they get all worked up because they can't wind down. I know its hard but hang in there it does get better..
Congratulations again I'm in such shock at how fast the second time rolls around, it does go by way too quick :)