Nursing mommas - comforting themselves with the nipple?

Bubbles412

My LO is just over 3 weeks old and I am EBF. I have noticed, espcially at night, that she will wake up and scream and scream until I go to breast feed her...at which point she will suck for MAYBE 3 minutes and then fall back asleep with my nipple in her mouth. If I try to put her down, or even just move her off my breast, she starts screaming again. I think she is using my nipple as a comfort...she won't take a paci and we have tried three different brands. I don't want her to get used to having to use my nipple for comfort...any tips or ideas?