Can a person have burning in the penis for months?
Yes, that is possible and may have many different causes.
Months? Maybe you have something more than genital herpes.
Your first reaction is your worst but overtime it won’t be as bad. The outbreak will last longer if you do not get an antiviral to help your body fight off the disease. So I would recommend you seeing a physician who can prescribe valcyclovir or another antibiotic.
Eat health & exercise if you are living an unhealthy lifestyle more than likely this disease will worsen, and if your diet is high in arginine the outbreaks will increase. Also, try to keep your stress levels as low as possible just like shingles, genital herpes is apart of the herpes simplex virus which is triggered by your stress levels being abnormally high.
Best of luck to you.