I started to have pain in my penis many years ago, it felt if it was at the tip but when you felt it was not coming from the penis. I now believe it is coming from the urethra or external sphincter. The pain makes me feel like I have to pee all the time even just after going. It lessens the pain when I am actual peeing(muscle relaxed) I had high antibiotics treating for infection and prostatsis. I even had a surgery to unblock some things. It did not work and I learned to live with the pain which came and go. I was having more urinary frequency, urgency issues as time went on.
Two years ago I got an MRI of the prostate it showed a high probability of cancer. I was extremely stressed because I had ignored the pains in my pelvic area. The pains in the pelvic area became constant and I was getting burning in the rectum area. At one point just before my biopsy I got pain throughout my pelvic area, it was inflamed. The urologist said it a nerve issue. This started for the first time that my issues could be the pudendal nerve.
I had the prostatectomy and the pain in the perinium area disappeared (I believe it was the seminal vessels which were clogged due to prior surgery to shrink my prostate) and for one week when I had the catheter in I was sleeping through the night. I was extremely happy and thought the pain at the tip of the penis was the catheter and the rectal pain feeling I had to go giving me pain and feeling I still had to go. When I actually had to go the pain became unbearable and I would have accidents. I ended up having sitting pain and penal pain. I started physical therapy and stopped doing Kegels. The therapy helped lessen the pain and relax the external sphincters for rectal and urinary. I started the Kegels and the pain came back in intensity. I stopped doing Kegels, avoid sitting, sit on a doughnut. I am on Cymbalta for pain and depression, and oxybutin for urgency and have both urinary stress and urgency.
My two priorities is lower the pain to a tolerable level so it does not stop me from seeing my grandkids and to be able to sleep. The urinary incontinence is secondary and I can manage it by wearing protection.
I have gone to pain management and am going to get a pudendal nerve block. This will give me a better idea if it is pudendal neuragia and it may also lessen the pain for a period of time

I am not a doctor but you should look into pudendal nerve pain. I wish someone had mentioned it to me many years ago. But back then it was not looked at.
Best wishes and wishing you happiness always