What Could Be Happening To My Dog?
If an insect has bitten your dog, it may contract Lyme disease. This is a disease that can affect the skin, heart, joints and the nervous system. It is important to treat this straight away as the treatments provided improve the liver function and build up the immune system of the animal, whilst killing the bacteria. There is a chance that it is a fleabite, but it is unlikely to be ringworm. Ringworm doesn't show the target area (the puncture marks).
And If It Is Ringworm?
Ringworm tends to be raised and not flat but it would still be worth checking with a vet to make sure. If it is ringworm the vet will prescribe a medication in cream form called Miconazole. This can be applied to the affected area by simply dabbing it on. If you rub it in, the ringworm could spread. Ringworm is not actually a worm, but a fungal infection.
What Else Could Be The Problem?
The other possibility is that another dog may have bitten yours if it has been involved in a fight. Any canine antiseptic would help to treat this, and antibiotics would also help to reduce the discomfort the dog is feeling. From the description it would appear it is an insect bite but the vet should be visited as soon as possible to rule out ringworm or Lyme disease.