You should avoid any strenuous exercise for 4-6 weeks. Generally I do not let patients resume fully activity until they have had their post op exam and I have assured they are fully healed. Strenuous activity can place significant tension on the suture line. Your sutures and skin are delicate so that amount of tension can easily cause a separation and result in a poor result. You paid a lot and have gone through a lot to achieve your ideal cosmetic result. There is no reason to risk that now. You can walk for extended periods at a slow rate if you really have to do something.
It looks like a small separation. Apply neopsorin and it should heal fine since its on the mucosal surface.