Testosterone therapy has various risks, including:

Worsening sleep apnea — a potentially serious sleep disorder in which breathing repeatedly stops and starts.
Causing acne or other skin reactions.
Stimulating noncancerous growth of the prostate (benign prostatic hyperplasia) and growth of existing prostate cancer.
Enlarging breasts.
Limiting sperm production or causing testicles to shrink.
Stimulating too much red blood cell production, which contributes to the increased risk of forming a blood clot. A clot could break loose, travel through your bloodstream and lodge in your lungs, blocking blood flow (pulmonary embolism).

Also, some research shows that testosterone therapy can increase your risk of heart disease. More research is needed.