@Dazzle Based on reading a few sentences on a message board and knowing nothing about your history or presentation, sounds like it could be likely 1 of 3 things.
1. Heel strike or toe strike versus a mid foot strike. Have a friend or your phone film you running about 20 paces. See where you make first contact. It could be a simple biomechanical fix by adjusting your foot strike which will reduce or eliminate repetitive trauma (ie. repetitive excessive stretches) with every step to the likely tight, weak ankle stabilizers, calves and even up to the popliteus and distal TFL.
2. Similar to above, but assessing the other end of the leg. Piriformis syndrome or even just piriformis tightening is very common when someone takes up running after some time off, and can change your hip positioning, which will alter your mechanics all the way down to your ankle and circling back to impairing your foot strike and ankle positioning.
3. Could be as simple as calf strains (similar to how your legs hurt a lot after squatting for the first time after a break) and over time as you stay consistent with the running the tissues will be able to meet the demands.
I don't think it's anything related to compartment syndrome.