Good. Your husband may have an oddly placed lymph node that got nicked, or it could have been an allergy to the plastic in the syringe, that was actually there since the shot, and only noticeable 10 days later. Really, a doctor has to look at it. 6 SD posters will give you 12 different possibilities.
And it could still be unrelated. I had a painful swelling in my arm once, that seemed unexplainable, until it was followed two days later by a toothache, and I realized I had lost an old filling, and now had new decay in the place it had been-- a huge hole, FWIW. I needed three days of antibiotics before a dentist would think of treating it, and he wanted to do a root canal at first. After several x-rays, he agreed to just replace the filling, but I had to sign a waiver that I might still need a root canal.
It’s been 13 years, and the filling is holding up fine. Boy, did that dentist, who filled it on a weekend, and was not my regular dentist, get a glowing Yelp review.
Anyway, the dentist confirmed that yes, lymph nodes can swell painfully in reaction to a cavity, particularly one in need of antibiotics.
Not relevant to your husband, obviously, but just another example of how lymph nodes in your arm can do all sorts of things: I had very painful left-side mastitis when my son was about 5 months old. Second day of it (and at the doctor), and a swollen, red ring around my upper arm on the left side. Massive PAIN in the left breast, but nothing obvious on visual inspection.
Left was his favorite side, too. 24 hrs worth of codeine, and an series of antibiotics, and I was fine. Doctor advised additionally OTC NSAIDS for swelling.
Sorry for going on, but trying to show that is could be such a great variety of thing, you need to see a doctor.