It does sound a lot like pinworms and it is quite common in young children. My daughter has had them twice. We took her to the doctor and although she looked at her bottom she could not definitely diagnose without actually seeing the pinworms. She told me to wait until my daughter was asleep and to take a flashlight and look at her bottom (anal opening) and sure enough that night I saw tiny little white squiggly things. Bless her heart, no wonder she was itching so much. Then the doctor phoned in a prescription. The medicine worked and I also had to wash all her bed linen and vaccuum really good. After a couple of days my bottom was itching really bad and so I had to take the medicine, too.
The nurse told me the eggs get under their fingernails and end up in their intestines when they put there fingers in their mouth. The eggs hatch in the intestine and the pinworms come out of the anal area at night whent he child is sleeping.
Like I said, my daughter has been through this twice and now I am very careful to make sure she washes her hands frequently and I use a fingernail brush when she's been playing outside.