There could be more than one cause, but I suspect it could be venous leak.
Venous leak is where the blood is able to escape the penis and back to the heart via your veins where you can't get hard enough or maintain an erection long enough. If healthy, you are relaxed and stimulated, blood rushes into your penis, causing the penile tissue to fully expand. When the tissue fully expands it pinches the veins shut, trapping the blood inside your penis to maintain the hard erection. If you have scarring, then this takes away the elasticity in the penile tissue preventing it from fully expanding, thus it leaves the veins open enough where blood can escape.
First, if minor enough, this can be compensated for with a bigger rush of blood into the penis, from my understanding, so Viagra could come into play there. However, there are also new attempts coming out these days to find a curative solution, including PRP injections directly into the scarred tissues (platelet-rich plasma) and other treatments.
I believe masturbation can cause scarring, especially depending on how you masturbate. For example, don't jerk your penis back and forth - it can cause scarring and even pinch an artery at the base causing a localized blockage. So I would try to stop or greatly reduce masturbation. When you do masturbate, do it correctly. And if there has been new irritation due to masturbation, try to take supplements to encourage the best possible healing of this new injury, so when it heals up it forms the least amount of scarring as possible or no scarring.
Last thing - I would keep searching for urologists. There are different things you can try, so keep at it!