Did he have any back or pelvic injuries in the accident?
Does he have sensation with his penis?
Does he have any loss of control over bowel motions?
What sort of volumes does he pass when he passes urine without warning?
Thanks for the extra information.
There are some things that need to be ruled out which hopefully his doctor has already considered.
The first is whether there is any spinal or root nerve damage, as there was no mention of lower pack injuries and he has sensation of the penis complete with control of BM's then I think we can rule this out.
The next is whether there is any infection. You mention normal volume and you do not mention anything significant about the urine such as strong color or odor however if a sample has not been tested recently for infection then this should be arranged. If the penis is very tender then an examination and swab may be required to rule out a local infection.
Concentrated urine can also cause irritation of the badder and this should be avoided by drinking plenty of water, however as urine volumes are normal rather than small amounts then concentration most likely is not a cause.
That leaves us with a post-catheter situation. It can take some time to retrain the bladder after having had an indwelling catheter.
One way to help is to work on the muscles that are involved in urination. The pelvic floor muscles are strengthened with Kegel exercises. This website is used by mens with incontinence and ejaculation problems however it explains the process in easy steps: here
If there is no improvement with the medication and exercises then he should see a urologist and he may need some investigations into bladder capacity and flow control. A physiotherapist with special interest in urology can also help with bladder exercises to encourage bladder and signals for urination. This is a slow process but he should see some improvement after a while. He is still early days after his injuries so try to take each day as it comes. Modern pads are much more discrete and should give him some confidence to get out and about in the meantime.