Welcome to Justanswer! I am Dr. Altman and happy to assist you both today!
So sorry to hear Beau's not feeling well. You mentioned his testes (scrotal area) and penis are swollen...just to verify that it's not actually his prepuce ('sheath' over the penis) that's swollen versus the actual penis inside. (For you to say his actual penis is swollen, would assume it's out of the sheath and swollen...as in an erection that wont' go down or the inability to retract his penis--I'm assuming you mean his sheath and scrotum are swollen, however)
Before going into any further detail, please know that a dog with the problem you've described has something potentially serious going on and would be best treated by having a hands-on veterinary examination and therapy prescribed based on a diagnosis. In my experience, this is not something likely to resolve on it's own.
Furthermore, due to the areas involved, there's concern of too much swelling cutting of blood supply and/or urine output. Either way, it's bound to be uncomfortable for poor Beau.
Swelling of these areas can be due to problems associated with, trauma, infection--a lot of things ending in "itis"-- (cellulitis, balanopothitis/posthitis, epididymitis), obstruction of lymphatic flow or drainage, obstruction of blood flow( eg: thrombus/embolism--ie, blood clot), torsion (of testicle(s)), low blood protein levels (hypoproteinemia), ruptured urethra with subcutanous fluid accumulation, inflammation, herniation, and rarely cancerous involvement (not as likely in a young dog).
Swelling such as described is called edema and may be further categorized as pitting or "non-pitting" edema, based on how springy the tissues are when a finger is gently indented into the tissues--non-pitting type does not 'dent' appreciably and the pitting type does indent , gradually filling back in... Other clues as to origin of the edema include: are the swollen tissues discolored or bruised? Are the swollen areas warm , cool or normal temperature to the touch? Are these areas painful or uncomfortable? Is Beau running a fever? Acting sick or acting normally? It's great he is eating/drinking... Bowel and urine patterns ok? You can cross some of the causes of scrotal and preputial (sheath over the penis in dogs)swellings based on some of the answers above sometimes.
Brucellosis is a bacterial disease that is serious and can be the cause of the symptoms you describe. A blood test can be submitted by your veterinarian to check for this. It will not self-cure. Tick-borne diseases may cause vasculitis, as can heartworm disease among other things, so again- diagnostics to help detect this may be helpful in choosing a treatment plan. Other infections may be causing edema by cellulitis (unnoticed bitewound or puncture, grass awn or other foreign body stuck in prepuce etc)...
Trauma to the area may result in swelling, testicular torsions happen on occasion and may also result in significant swelling in the area. Herniation at the inquinal canal level could potentially results in swelling "downstream" to those areas (ie, scrotum/prepuce)...Again, an exam may help define this possiblity better . A peek with an ultrasound probe may be helpful...
There are many causes for blood clot formations (coagulation issues, trauma etc) that may obstruct venous drainage. Treatment and prognosis would depend on the underlying cause. Low protein levels resulting in localized edema (versus generalized edema) is possible but not too common...Severe intestinal worms may cause anemia and/or low protein levels in the blood , as well as liver disease, kidney disease or generalized gastroinstinal disease --all of which would likely require some diagnostic tests to pinpoint.
If perchance, poor Beau is really suffering from an extruded penis that he cannot retract back into his sheath (resulting in exposure and swelling), again--this is a situation that requires veterinary intervention and could be life-threatening if untreated.
Hopefully this gives you a place to start but I would strongly recommend an exam to hopefully determine the cause and begin appropriate treatment to reduce the swelling and get Beau more comfortable asap
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