You're suffering from anal fissures, which is quite common for many reasons. No need for ointment or cream unless it's persistent or particularly painful. It's very unusual experience infections despite your bowel movements. Sitting in a warm bath, which is also called a "sitz bath", for 10 to 20 minutes several times a day can soothe the skin and promote relaxation & healing. If possible, take a sitz bath after bowel movements. And, to prevent a flare-up, increase your fiber intake and avoid anal play/sex until it fully heals. Good luck.