You might want to consider a few questions while making these plans.

First, will you need access to your medicine during travel?

If not, then when will you need it, and can you medically afford to be without it for an additional day or two in case of misrouting of baggage?

If the medicine is delayed, damaged or somehow contaminated, have you made plans to obtain replacement at your destination? Do you have the necessary documentation to do so?

If you will be carrying it on, will you have enough cooling to handle IRROPS situations like being delayed a large handful of hours, being re-routed through a connection, being diverted, etc?

If you use ice to keep the medicine cool, and have a stop (planned or otherwise) that requires re-screening, you will need to have a way to pour off the melted water. Ice is accepted as long as it is still solid; semi-melted ice is limited to the 3-1-1 rule. Here is the relevant link from the TSA:

https://www.tsa.gov/travel/security-.../gel-ice-packs

Using the information on that page, it seems like gel packs are the way to go, along with a sufficiently insulated container to last your planned trip length plus, say, 24 hours.