So his injured penis can heal an alpha-male is put on libido removing medication, disrupting his win at all costs mentality and threatening his chances of becoming street luge champion.

Sorry, I put DO SOMETHING in brackets and it didn't show. Here's what I meant to say:

When a confident street-luger injures his penis and is put on libido reducing meds, he must ::DO SOMETHING:: to win the championship.?

Fill in DO SOMETHING with the action he must take to overcome the effects of his meds, and win the championship.

Howabout: "When a confident street-luger injures his penis and is put on libido reducing meds, he must to win the championship."

The street luge champion hits you like a brick at the end of the logline. It is a crucial part of information to do with the goal of the character. But the logline suggests it will about his world once he has given up on the luge championship because of the injury.
Use of the word alpha male makes me think of him as a prize A chimp, but they maybe by personal taste at the use of that word.