We flew on Delta last time, and my mom had ALOT of injectable medications with her. She put most of her insulin syringes in her checked bag, but still had several in her carryon. She put them all in a ziplock bag. She also had numerous vials of pre-filled syringes. She put them all in a gallon ziplock, with the prescription label visible. She placed them all in their own bin, and let the security agent know there were meds coming through. She also had insulin vials in a soft-sided cooler with frozen vegetables to keep them cold. We had no problem at all at any security checkpoints.
For the return trip, your SIL won't have frozen veggies to keep her insulin cold! I would bring a ziplock bag and fill it with ice at the airport. There should not be a problem with it going through security, but if they do have an issue, just dump the ice in the trash and refill the bag with more ice after passing through security.