I have a small, dime-sized red spot on my shoulder,
Hello and welcome to ask a doctor service. I have read your query and viewed the image.
I can see a red scaly oval patch of skin. It seems like a fungal infection. I suggest you to apply an OTC topical antifungal e.g clotrimazole 1% cream or miconazole 2% cream, twice daily for 2 weeks.
Hope I have answered your query. Let me know if you need any more assistance.
Regarding fungal infection
Yes, pets can be a carrier for dermatophytes- the fungus which causes superficial fungal infection.
let me know if you need any more assistance