There is a hole near my dog’s rear that has broken open

A hole near the dog’s rear that breaks open is generally anal gland inflammation or an anal gland cyst. Try squeezing with tissue; if pus flows, clean daily until dry, rinse the wound with peroxide or iodine to disinfect, then apply erythromycin or another ointment, avoiding rubbing, for 7 to 15 days.

If the dog shows low energy or appetite, do not treat at home; gland inflammation can cause body-wide inflammation, so see a vet, and severe cases need cyst removal surgery.