OP, I remember when my daughter (who is now 15 months) was around that age and it was truly exhausting, emotionally draining, and confidence destroying. It's so heartbreaking to see your baby so upset and trying everything to soothe, and it just doesn't work. Made me feel useless sometimes!
There are so many different reasons as to why baby might be crying and if it's more than one thing, it's hard to figure it out. I do know there is something they call 'period of purple crying' which is a term used to describe colic or even just general fussiness. Colic is one of the more common reasons as to why a young baby may cry, as far as I know.
I believe my daughter had bad colic, and that's why she went through periods of near constant crying. I'm sure you already know all about colic but I just thought I would make that suggestion in case.
My daughter was also teething at 12 weeks, which added to her discomfort! There are also studies which suggest that crying in babies is sometimes not actually due to any particular physical issue, but it's rather a developmental process they must go through to bond with the mother and receive affection/comfort.
I was told by my health visitor when our baby was newborn, that during periods of extreme fussiness, it's good for the father/friend/relative to take Baby away for a moment and let baby calm down, be away from your scent, and have a distraction.
As long as you have checked her temperature and it's normal, check her skin for any marks/rashes, and she is still willing to feed I would say it sounds like a severe bout of fussiness and it will pass (obviously if your instincts are telling you to take her to docs, do that by all means).
Everything will be fine and it does get easier, sometimes!
Sending you hugs x