That sounds like my little guy. The Happiest Baby on the Block routine did help some (swaddling especially): swaddle, suck (breast, bottle, or pacifier), shush (louder than they are crying), sway, and whatever the other one was. And he still cried a lot and didn't sleep very long. We thought there was something seriously wrong with him, but the pediatrician kept telling us he is just being a baby, and it got better eventually. If she's eating every 2 1/2 to 3 hours, you're actually getting away better than lots of new parents-they're theoretically supposed to eat every 2 hours or so at that age (mine never did, and he gained 3 pounds the first month breastfeeding pretty exclusively). Now, if she's inconsolable after a feeding, you might try formula (if nursing--or an extra ounce or two if you're bottle-feeding), they sometimes just want more and she could be having a growth spurt.
Elishai hated the swing and the bouncer, in fact, he still does (he's almost 6 months old, and is totally fearless). Some babies are really sensitive to external stimulus. It really helped for us to reduce the number of colors, objects and noises he was exposed to after we figured that out (after about the first 2 weeks of continuous screaming). They don't need to be on a bright play gym with the lights and the music and things waving at them at this age--some babies are really freaked out by the commotion. You can try giving her her tummy time on your stomach-the closeness is appealing for them and plus it encourages her to lift her head to look at your face.
Last, have you started some kind of bedtime ritual for her? It helps babies to understand the difference between day sleep (naps) and night sleep. Somewhere in the next couple of weeks, she'll start to be able to sleep differently at day and at night (which is to say, she'll still wake to eat at night, but hopefully go right back to sleep, whereas in the day, she'll have some awake time between shorter naps). We use the standard bath, book, lullaby, feeding ritual, and it does help. Not overnight, unfortunately.
Actually, really last: try to make some time for yourself. This age is so hard on you. Right now, she probably sleeps fine in her carseat, so go out and do things. If she's asleep at a mealtime, go out to dinner with your SO. Go shopping, get a manicure, whatever it was you used to do for fun.
Good luck--feel free to contact me if you have any questions about the babies who don't sleep like babies problem!