Prospero. I had a sister that was highly dependent on insulin. In the short term, use a nice big cooler and stock up on ice. In the longer term, understand your options. A good cooler that is big and stocked should last a few days.
I am Googling "Insulin Coolers". There are some good solutions for maybe three pens, but for a week or so of no power the options drop off drastically. So I am looking at basic DC powered small refrigerators and realize I have my work cut out for me.
We have several battery operated fans for our comfort when the power is out, and flashlights, etc. We have propane to cook food before it spoils, and canned food for regular meals. Instant coffee and creamer of course, and plenty of water (for a week anyway). So keeping her insulin cool is the main objective we need to nail down.
You may want to look into Cooluli. The one I linked, while not the most visually appealing, is at least available now via Prime One-Day for the Orlando area. I have all 3 sizes of their mini fridges, and while they're not cold enough to keep food for extended periods, they will work for keeping insulin cold enough for several days. My mother-in-law uses insulin, and we actually keep one of these plugged in and cooled for use in the event the power goes out. Also comes with plugs to use in the car or even USB power banks. Like most thermoelectric fridges, they only cool to about 40 degrees below ambient, so keep that in mind when using them.