Hi Danielle! Thanks for bringing your question to planDisney.
We often travel with little ones, who require a lot of packed extras, including medicine. We typically keep their medications, including prescription medications, in a travel pill dispenser. It's never been an issue for us going through security. There's nothing currently in the
park rules about bringing medication into the parks in its original container. However, park rules are subject to change, and it's always up to the Cast Member working to decide at their discretion what can and cannot safely enter the parks.
First Aid often has some of the medications you might need, including small emergencies you didn't plan for during your day. Over-the-counter medication, bandages, and additional remedies are often available. We've popped in for a bandage after a small tumble, medicine for a headache, and cream when my son experienced hives from a minor allergic reaction. The professionals at First Aid are extremely helpful.
I hope this helps!
Elizabeth