Itching with soreness after friction from a toy, especially if it wasn't fully cleaned, is usually local irritation or sometimes a mild yeast flare, not an infection from the device itself. No pain while peeing or bleeding is reassuring.
Next Steps
Keep the area clean and dry, avoid further friction for a few days, and clean sex toys thoroughly before and after each use.
Health Tips
See a gynaecologist if the itching doesn't settle in a few days, or if you notice discharge or swelling.