Fridge is the way to go, though not the door because of temperature swings. The prescription version has stabilizers that let it sit out, but the grey versions do not. Even the newest prescription version is only rated for seven days at room temperature, and older ones were meant for immediate use.
Debating whether Tesamorelin needs to go in the fridge after mixing or can stay at room temperature. Curious what others think. Checked the pH both ways and got 4.5-5 either time.