In the flashback to Shay's first day at Firehouse 51, she states that she came from Firehouse 87. This is the same station that, in the Season 2 finale (Real Never Waits (2014)), Casey tried to convince Dawson to go to as a Firefighter Candidate instead of Firehouse 105.
Casey tries to pull some strings to get Dawson into a different firehouse from the one she will be assigned to when she becomes a firefighter candidate. Casey and Welch, the other firehouse's lieutenant, have had run-ins, and Casey doesn't want his fiancee to have to deal with an uncaring, sexist superior officer. Dawson rejects Casey's help and says that she wants to be treated like any other candidate and doesn't want any special treatment.
In the flashback at the beginning of this episode when we see the day that Shay joins Firehouse 51, we learn that she has spent her first two years as a paramedic in the firehouse in Logan Square. This is the same firehouse that Casey tries to get Dawson transferred to, so it's possible that Dawson has an additional reason for refusing Casey's help: She doesn't want to be at Shay's former firehouse and have to be around strangers who knew Shay before Dawson did. Perhaps she wants a fresh start and doesn't want to be reminded on a daily basis of her deceased friend and partner.
In the flashback at the beginning of this episode when we see the day that Shay joins Firehouse 51, we learn that she has spent her first two years as a paramedic in the firehouse in Logan Square. This is the same firehouse that Casey tries to get Dawson transferred to, so it's possible that Dawson has an additional reason for refusing Casey's help: She doesn't want to be at Shay's former firehouse and have to be around strangers who knew Shay before Dawson did. Perhaps she wants a fresh start and doesn't want to be reminded on a daily basis of her deceased friend and partner.