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I hope that I can provide some assistance for you and your hamster.
The kind of signs you are describing--fur loss, scratching, and a rash--are consistent with skin allergies. Allergies can be the result of something new in the environment such as a new type of bedding, cleaner, or food, or can be the result of inhaled allergens in the home such as dust mites or pollens. Some hamsters with allergies can develop a skin rash, or skin infection, secondary to the allergies as well. Skin infections further increase the itchiness. The most common treatment for allergies are either antihistamines or steroids, with antibiotics being used if a skin infection is present. These treatments can be prescribed by your veterinarian. Identifying the allergen and removing it from the hamster's environment also is very helpful, but determining the cause of the allergy can be very difficult. If you recently changed the bedding or food and suspect this is the culprit, change back to the old bedding or food.
Additionally, some skin mites can also cause the kind of itchiness and fur loss that your hamster has--the only way to know for sure on the mites is to take him to a veterinarian who can do a skin scraping and look at the skin cells under the microscope.
You also want to be able to rule out a skin irritation that could be the result of a dirty cage or the result of the hamster having diarrhea or urine scald. If the cleanliness of the cage and hamster has been good, it is unlikely that these are the cause, but you might want to check and make sure, as these are easy to remedy.
I hope that this has been helpful to you. Good luck with your hamster.