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I'm sorry to hear about Chad's condition. Without seeing it, it can be difficult to determine what is going on. If he is otherwise comfortable- eating, drinking and able to get around you can monitor it for the next day or so but if he is not eating, if the swelling gets worse or if he seems to be more painful, he should be evaluated by a veterinarian. Constipation shouldn't be an issue unless he is straining to defecate and cannot pass stool. If he is not trying to defecate then he is not likely to be constipated.
Since there is a history of trauma, he may have sustained an orthopedic injury and the only way to evaluate this would be with radiographs ("X-rays"), however other possible causes of swelling include a lack of lymphatic flow due to blockage, a tumor, an insect bite (or snake bite depending on the area) or allergic reaction and soft tissue injury such as a muscle strain or tear. Unfortunately, dogs do not handle over the counter drugs as well as humans do so there is nothing I can recommend giving him for pain. Ibuprofen can cause toxicity and side effects even at therapeutic doses and the therapeutic range is very narrow.
If he is uncomfortable enough to warrant pain medication, he should be evaluated by a veterinarian so that pain medication can be prescribed and dispensed. If the leg appears to be bruised, he should be seen by a veterinarian as well. Testicular torsion is not very common in dogs and is usually evident by a largely swollen and painful scrotum. If his testicles and scrotum look normal then I wouldn't worry about testicular torsion at this time. If you have further questions, please feel free to ask. If you are satisfied with my answer, please rate me as this is the only way the website will credit me for my time. Best of luck to you and Chad! I hope he is feeling better soon.