Hi there,
My LO cried too as soon as she was wrapped, i think they know sleep is coming and this is their way of letting of steam. Or saying please just let me go to sleep.
You say you don't put her in his cot until she is asleep? Have you tried shh/patting her in crib? Now is a good time to start teaching independent sleep. If you think of sleepiness in a scale from 1 to 10 — 1 is full-throttle and 10 is out cold (like your are doing now). Start backing off from 10 slowly and the goal is number 7, when you lay her down to sleep in her crib.
Sounds like she is going thru 1 sleep cycle (45min) then can't (or doesn't know how yet, she is still young and learning) to get herself back to sleep.
Have you tried either shh/pat to get her back to sleep when she wakes or going in before she wakes and trying wake to sleep method?
Here is a thread on the method: