It is quite Posible that infection has occured near your genitalia. My advice is to Use an antiseptic lotion like dettol and consult your health care provider. As nothing surely can be said unless viewing.
These red linear marks are formed after shaving. It is a good sign that hairs are growing . In my opinion usiing creams is considerd as a better option Regarding hair removal of genitalia.
I advice you to maintain hygeine and also take antiseptic lotion . Take Povidone lotion And after washing genitalia apply it .keep cotton piece over it .and tape ot. In my opinion this has to be done twice . Maintain proper hygeine.
Plz let me know if U Need more information