It would be good to get at least a second opinion on your situation which sounds like an injury to the shaft of your penis from your description. Seeing a urologist and getting an ultrasound of your shaft would be worthwhile. Since the doctor you visited did not refer you, you would need to be referred by another doctor or contact a urologist on your own, if possible, especially after three weeks with no improvement. Luckily, you can still urinate and pass semen.
I agree with YardBull. See a urologist as soon as possible and get an ultrasound as soon as possible, which I think can identify scarring if there is any as well as looks at bloodflow.
I would also add that you should do something today, tomorrow, as soon as possible, if there is anything, to try to have things heal in a way that forms as little scar tissue as possible, including any supplements possibly, wouldn't hurt. I know your injury was almost 2 months ago now, but I still think it's early enough to make an impact. One experimental thing I know about is PRP injections into the penis (into the exact spots of injury). This is where a doctor draws your blood, they "spin" it, then inject it into the problem area. It's supposed to add a lot of stem cells from the blood, which aid in healing, and possibly even overcoming some negative effects. It might be good to do this early. But you'll have to assess the risks of that on your own, and find the right doctor. I'm not sure if you'd be comfortable with a naturopath - I know that some urologists and naturopaths may offer this. Finding a urologist would probably be best.