If I were in your shoes, I’d consider delaying the start of Forteo until after your trip - unless your doctor feels there's an urgent reason to begin immediately. Starting right before trip can be tough, especially if you experience side effects while traveling.

Once you start the first injection, the pen is to be discarded after 28 days per manufacturer Eli Lilly, even if a small amount of liquid remains.

Traveling with Forteo is entirely doable, but it takes planning. I've traveled with Forteo many times. There are quite a few medical coolers on Amazon designed to maintain the cold chain (36-46°F, or 2-8°C for Forteo) that are TSA-approved. You can find several threads here discussing this topic. Lilly does allow a cumulative total of 36 hours at room temperature under 77°F (25°C) when refrigeration isn't available.