What type of holster and position do you carry in when not running? Do you need to carry concealed, or is open carry an option?
I don't run, but I walk and cycle some on a casual basis. I have an old Galco fanny pack I use for activities like that, purpose-built for left-handed carry, which holds a single-stack sub-compact .380 I carry quite a lot, along with a spare mag, and various other stuff like keys, phone, wallet, etc. There are similar purpose-built packs available nowadays, or you can rig one up yourself with a kydex pocket holster and some paracord.
Many people are using the PHLSTER Enigma to carry AIWB without a belt, so in gym clothes, scrubs, or whatever. Depending on your body type it might be worth looking into.