Neosporin is fine, but peroxide is irritating. It is good for removing blood, but does not disinfect skin and slows healing.
The important question is why is the dog itching. Fleas are the most common reason. Does he have fleas? Are you using a product that kills fleas? If there are fleas, the first step is getting rid of them. There are several good products on the market that can be used once a month. There are a lot of OTC products that do OK if only a few fleas are around, but are not effective if there is a flea infestation. Tick bites are another bug that causes itching and generally are killed by the same products that kill fleas.
If the itching is causing the sores, they are commonly called hot spots or pyotraumatic dermatitis. These are skin infections caused by the trauma of itching and bacteria. Treatment is to carefully clip the hair away from the spot and clean the area with a cleansing solution. Bactine works OK. Then apply a topical antibiotic with steroid. Vet preparations are called Panalog, Dermavet and other generics. Alternatively, Neosporin and an OTC 1% hydrocortisone cream/ointment help. Sometimes systemic antibiotics and steroids are required.
Itchy skin can also caused by mange mites, fungal infections including ring worm, some bacterial infections, skin tumors, food, inhalant allergies,irritating chemicals, etc..
If OTC and home remedies don't work, a vet exam would help find a specific diagnosis and more effective treatment options.
Drooling can be secondary to peroxide, Neosporin or irritants that could be causing the itching.
Let me know if you have follow up questions.
The carpet fresh could have caused the drooling. Other things that cause drooling are mouthing toads, many things that taste bad, infected teeth....
I don't understand the question about how much extra is this going to cost.....
You indicated that you would pay $9. When you accept the answer, this is what you will be charged. Only accept once. You don't need to accept each individual response you get. Also, you should post questions only once. Sometimes people post multiple times and get answers from multiple people.
Taking the collar off was a good idea.
The antibiotics should start helping with infections within 12-24 hours. It takes longer for the sore to heal, but improvement is usually seen within a few days.
If he is still itching, the itch needs to be stopped. The antibiotics will help an infection, but will not stop the itching once it has started. This may require a vet visit, but I'll give some other treatments that sometimes work.
Benadryl ( diphenhydramine) - Dose 1-2 mg/lb 2-4 times a day. I don't know the size of your dog. If he is small, you'll need the children's liquid. Large dogs (over 45 pounds) can get the adult 50 mg tablets. This will make your dog sleep more than usual, which is part of the reason it helps. I prefer to use the lower dose and give it 1-2 times a day. Benadryl also comes as a spray that could be used on the itchy sores and often helps.
Hydrocortisone ointment 1% - This is sold OTC for humans. It doesn't work as well as the vet preparations that have more effective steroids mixed with antibiotics and antifungals. I like to use the hydrocort along with triple antibiotic ointment.
Bathing with oatmeal pet shampoo or other that helps control itching helps some dogs. Ask your groomer about products.
Essential fatty acids (fish oil) can help with itching caused by dry skin.
If the easy things don't fix the problem, you may need to have your vet take a look.