E.J.
She is definitely not manipulating you! Babies don't have that capacity until they hit something like a year old or later.
We have a similar situation. My 4 month old son does not sleep nearly as well as his sister did at this age. However, I was doing some research on reputable websites (Mayo Clinic, etc.), and found a lot of helpful information. 1) Most first born children sleep longer earlier than their subsequent siblings. 2) 80% of children do NOT sleep through the night before 1 year old. (Despite it seeming like everyone else's child is doing. Everyone else is probably exaggerating.) 3) If your child is breastfeeding, until 6 months you need to assume that if they wake up at night, they are hungry.
We never did sleep training with my daughter but she naturally slept 10 hour stretches by 4 months, 12 hours straight by 6 months. All kids are different, and colds/teething definitely throw everything off. I think also 4 months is a natural point for sleeping to get worse even if it was better at 3 months (if I remember from my research). Hang in there; I think it's just a matter of time! Good luck!