http://www.bigdogboutique.com/ProductCart/pc/tick_head.html
http://www.netwellness.org/question.cfm/39977.htm
which said:
"The tick head has reverse harpoon-like barbs that attach the tick firmly and the mouth has secreted a cement-like substance to hold the mouth parts in place. This accounts for why it is so difficult to remove completely. The head parts really will not get into your body, thankfully. Also, the red bump and itching at the attachment site is just a local reaction to a foreign protein in the skin and not a sign of systemic illness. Another happy fact is that if your husband removed the tick within 7-10 hours of its attachment to you, there is very little chance of the tick transmitting Lyme Disease or any other illness to you.
This is a tough question because there is no standard strategy. You have already waited two weeks. So you can keep waiting, disinfecting the site with alcohol or betadine 2-3 times per day and applying diphenhydramine 2% cream to relieve the itch until the head parts fall out on their own. The other alternative is your husband could attempt removal by first applying detergent to a cotton ball and rubbing it in a circular motion over the mouth parts to loosen the tick cement holding the head in place; then taking a clean needle, wiping it with alcohol, and attempting to lift out the tick head parts. "
http://www.nlm.nih.gov/medlineplus/ency/article/007211.htm
This site cautions to be careful not to leave the head in, but makes no mention of H2O2. It recommends antibiotic ointment.
So I have found sites that recommend seeking medical attention and sites that say the body will encapsulate it if it i left in the body.
Didn't see any medical sites recommending hydrogen peroxide. And from the description of the cement-like secretions around the head and the barbs, it wouldn't do th etrick anyway.