Doctor recommended cloth diapers

My sons about to be 5 months on the 4th well Sunday morning I called his doctor because I thought he had a chemical burn from huggies he told me to use neosporn well after 5 days it didn’t go away seemed to get worse so he got him in right away today and gave me some cream his diapers are rubbing against him really bad he recommended me to use cloth diapers but I don’t have a washer and dryer at home so I don’t think it’s really an option for me to do that because I only have time to go to the laundry Matt every 2 weeks. He’s a little over 18 pounds in size 3 diapers. Would it be possible for me to move him up a size in disposable diaper or what I can I do??