I know it feels like it is taking a long time, but she is still very little, and it's not unusual for babies to "nap" poorly at this age. True naps, lasting several hours in the crib, will probably set in around 4 months. In the meantime, I wouldn't feel bad for using the swing or bouncer to get her to sleep. You have to keep an eye on her, but it gives her a rest and you a break!
My now 5 year old napped like a champ in the crib from day one, but in patches of 30-60 minutes randomly after feeding. Around 3 months, she established a three nap day with naps lasting aorund 2-3 hours. I usually nursed her to sleep before laying her in the crib. My second daughter, now 20 months, would sleep in my arms or the bouncer for 30-60 minutes. Around 4 months she started resisting the bouncer and not sleeping, so I started putting her in the crib. It was a bad few days transitioning, but then she was set with her three nap day.
Start aiming for the 2-up 2-down rule. For instance, wake at 6, eat and play, and down for a nap at 8. After 2 hours of sleep, she should wake for 2 more hours before her next nap. It will take you awhile to get there, but that's the goal. Sounds like she is a pro at night sleeping, and I bet she even drops that 3am feeding soon. Congrats!
And to answer your question, she probably is tired and needs sleep, but she can't soothe on her own without feeling swaddled or without some white noise. Your arms or the swing give her that warrmth and comfort. I never wanted to but some people use swaddling and or white noise machines for this purpose. Also, you could read up on "Healthy Sleep Habits of a Happy Child." There is also a booth that focuses on the "S's" - swing, suck, swaddle, shoosh - I think. It replicates the womb based on the notion that the first 3 months is the fourth trimester. Can't remember the name of tha tbook, mayby "Happiest Baby on the Block"?