Hi pevie, it must be very hard on you.
My dd got separation anxiety from 5 months, It is earlier than the books say, but she behaved exactly like you described.
My dd was difficult from birth, like your dd, but with separation anxiety became almost impossible.
The mechanical swing worked for dd for a few weeks but at 7 mths, your dd might be too big for it. Try to borrow one if you can, although if she won't go in a pram or car, not likely she will go in a swing.
What I did notice was that when dd/ds got older, they would not go in a buggy/carseat for long times before getting fussy. The key was to take them out around naptime, and not at others. Does your dd fuss the second you put her in, or only after, say, 10 minutes?
Second the sling. But my dcs would only go in for around 10 minutes before fussing to get out. At least they were calm for those 10 minutes.
Have you read Dr Sears book If your dd has these traits, I found the book really helped me to accept the 'high need' baby that both my dcs were.
Whilst googling Sears, I also found his tips for soothing babies: here