I have drawn a cute little pup in Paint to give you an idea of where to look. Swelling in area 1 is suggestive of a dental abscess. Usually teeth develop an abscess below the gumline and become tender. These can rupture into the mouth or even from the skin outside of the jaw. What you may have seen as far as the "shell" of the tooth goes is either truly the outside of the tooth that's broken off or some dental calculus that broke off and dislodged from the mouth. If you saw something white, this is more likely to be a fragment of tooth than calculus.
Area 2 is below the jaw line and actually on the neck. This area, too, can be an abscess but is also located within the area where the lymphnode is located. It can be a very concerning sign when we see a very enlarged lymphnode, just so you're aware. That said, it's also common for lymphnodes near an abscess to become enlarged.
If you see a swelling that protrudes away from the skin, this is suggestive of an abscess and would benefit from being lanced and drained. If associated with a tooth, the tooth may need to be pulled and the area lavaged. If your boy does not receive regular sedated dental cleanings by your veterinarian, the chances of this happening are increased. While he's been on antibiotics, it's usually not enough to clear a deeply rooted infection like an abscess, and especially one that involves the mouth. Additionally, while penicillin is a good, broad spectrum antibiotic, it's not usually used for major infections like abscesses. As well, if it's along the jaw line there may be bone involvement and that becomes even more important to use an antibiotic that's useful at the deepest level (an example would be clindamycin). He may need something stronger, along with surgically addressing the abscess, in order for this to clear entirely.
I would also caution you against using Ibuprofen for him. This medication is toxic to cats and dogs at all dosages. By receiving it, dogs can have every symptom from anemia, gastric bleeds, liver failure to seizures and death. While I have no doubt that there is discomfort associated with this affliction, it is absolutely imperative to stop giving him ibuprofen. Even a child's dose, the 5mg that he's received, can kill him. There are lots of medications on the market that are tailored for the usage in dogs such as meloxicam, rimadyl, deramaxx, etc. Your veterinarian can prescribe one of the aforementioned medications to help with discomfort. Because he's been received ibuprofen, it would strongly urge you to opt to have labwork performed at this next visit to be sure that there are no lasting effects from receiving this medication. In some cases, transfusions, hospitalization and so forth are needed to treat the effects this medication has on dogs.
Whether it's an abscess on the neck or a swollen lymphnode, your best bet is going to be taking him to be seen by a veterinarian. They will need to address the possible broken tooth and potential abscess, as well as to be sure that the ibuprofen ingestion does not also need treatment. They should also be able to send you home with a different antibiotic and pain medication to help clear the symptoms he's currently having. If needed, a dental cleaning can also be performed. They will be able to give you better recommendations based on what they can see in his mouth. Even if he's a little opinionated at the vet and doesn't prefer to be handled, there are options available to make his visit an easier one despite the aggression that you've mentioned. As you well know, vets have to deal with everything from cute little puppies to the most aggressive feral cat. We often get naughty patients and it's just something that comes with the territory.
I wish you the best of luck with your little man. If my answer has helped you, please take the time to rate my service. If questions remain, please reply. Below you will find the photo I mentioned above.