Baby won't go to sleep without being carried around

Someone please help me. I'm so frustrated and at a loss. My baby won't go to sleep (day or night) without being carried around to fall sleep. This is what happens every day- I follow her early cues of yawning and wanting to eat, so I feed her and start to rock her and put her down before she gets all upset. But she won't fall asleep just from me rocking her (I try every potition in the book), so she gets frustrated and more tired, starts crying. Hours pass by, she gets overly tired, more frustrated, then needs to eat again cuz it's been so long. She might fall asleep for 10 mins here or there, but won't stay asleep long enough for me to put her down. (If I put her down drowsy but awake she freaks out.) Then eventually she might finally fall asleep after 4-5 hrs. We spend our ENTIRE day trying to get in 1 solid nap. It's okay if she likes motion, but I wish she'd like me rocking her or the swing, not just being carried around. :( I can't get anything done with her awake because she just cries super hard. I can strap her to me, but there's still tons I can't do with her strapped to me, including showering. I can put her down and let her cry for 5-10 mins so I can take a quick shower or carry down the laundry, but that doesn't solve the problem. I still am coming back to a super upset crying baby. Idk what to do. Last night I finally gave in and walked her around after every feeding to get her back to sleep because my husband is sick and I'm completely exhausted. Swaddled or unswaddled makes no difference, the pacifier pisses her off 75% of the time. We have a noise machine. I follow all "rules" of eat, play, sleep in the day, then quiet and boring with no stimuli at night. Once she's down she'll sleep okay- IF she's fallen into a good sleep being carried. If not, she'll seriously catnap, wake up, repeat the whole process. I've read about the 4th trimester and I get it feels like being carried around in the womb to her, but I can't live like this. She'll be 5 weeks old on Monday and I can't keep doing this for 2 more months. I can't hold her all day. I need to eat and shower and do housework. She also HATES being in the carseat. She'll fall asleep in the car as long as it's in motion, but if we stop at a light or go into a store she freaks out. Since her carseat clicks into the stroller she also hates stroller rides. I can't go anywhere or do anything. :'( Can someone please offer some advice or encouragement?