Hi, I'm Dr. Bonk. I'm sorry to hear about Doogie's troubles. Redness and moisture between the toes are usually caused by an allergy or irritation that the dog then licks and scratches and can lead to an infection.
The best treatment is to try to soak in warm water and Epsom salts. Place in a shallow dish and have Doogie stand or sit with his paws in the dish. Ten minutes a couple times a day, if he'll tolerate it, will be fine.
Epsom salt helps to draw out the swelling and redness and reduce the itchiness so that the dog will stop licking and causing more irritation.
You can then apply astringent or witch hazel between the toes. Both of these are drying agents that can also help reduce the itchiness and decrease the likelihood of an infection.
If you think it could be due to an allergy, you can try Benedryl at a dose of 2-3 tablets per 60lbs every 6-8 hours. The higher dose may cause some sedation, so it is best to start out at the lower dose and increase slowly if needed. The Benedryl will also help reduce the irritation.
You can still apply the Neosporin once the astringent or witch hazel has dried. These can be applied 2-3 times per day. Stop with the peroxide as repeated use can actually cause irritation.
If Doogie's feet don't show improvement, or if they get worse, start having a foul odor or become sore, you should take him to a vet for prescription products and further diagnostics.
I hope this helps. Please contact me with any further questions you may have. Thank you and good luck!