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Hello, Brian, and thank you for writing in. I'm sorry to hear about your Beagle being uncomfortable with the scratching.
I would highly advise using a good flea/tick preventative/treatment, such as Frontline Plus, Nexgard, Advantage, Advantix, or others. Fleas are terrible right now (as is common in the fall), as are allergies.
Fleas will commonly cause itching along the back and tail areas, but other things can also, such as allergies (i.e. pollens, molds, etc.)
If there are live fleas, you need to treat your Beagle (and any other pets you have, if any) with a good flea product for at least three months in a row, to get rid of all of the life cycle stages of the fleas. Also, clean the place you live very thoroughly - vacuum everywhere you can, including under furniture and cushions - to help get rid of the flea eggs, larvae, and pupae.
In addition, you can try giving regular plain Benadryl (or the generic - diphenhydramine) at 1mg per pound of body weight (so, if he's 25 pounds, you would give 25mg), every 8 hours to help with the itching. You can also use a dog oatmeal shampoo daily to help soothe the skin. Let the lather sit on for 10 minutes before rinsing it off to give the best effect.
You can try a product called Bitter Apple or Bitter Orange on the hair around the area he's chewing (don't put it directly on irritated skin). These products are safe, but they are a deterrent - they just taste bad so once dogs taste it, they are more likely to stay away from the area.
He may also need an Elizabethan collar (neck cone) to keep him from licking/chewing his skin until it heals.
Overall, it would be recommended to have him examined by a veterinarian so they can see exactly what the underlying problem is, and treat appropriately. If he has something like skin mites, or a bacterial infection present, he will need more specific medication to help - and only a veterinarian would be able to tell if those problems are present. Also, he may need stronger anti-itch medication, such as cortisone medications. But, you can try the things I mentioned previously if you are unable to get him seen right away, and you want to try and help in the meantime.
I hope this is helpful. Let me know if I can assist you further.