Fleas aren't terribly fond of a human and given the choice between a dog and a person, they'll take the dog every time. It sounds like you have a significant infestation and they may be making a pit stop on you and in your clothes/bedding/furniture.
A long shower and shampoo should remove them from your body and a regular laundry will kill them on your clothes.
In order to really eliminate them - you have to start by treating the outside of your home. Keep the area mowed and well watered. Fleas cannot thrive in water. Set up your sprinkler system to go off every other day long enough to really soak the area.
To treat your pet, just wash them. Any mild (baby, no tear formula is what we use) shampoo will do. Lather up your pet (avoiding the face! If you see fleas go onto the face, just pick them off and drop them into the soapy water) and let it sit for 10-15 minutes. Then rinse a couple of times and repeat every 2-3 days to be sure you break the flea life cycle.
For the inside of your home - forget the bug bombs, flea sprays, powders and carpet treatments. They don't really work and can be dangerous http://www.wildlifeprotection.net/everything/eduFleas.html and http://www.nrdc.org/health/effects/npets.asp
Vacuum daily to remove flea larvae and eggs from the carpets, furniture.
Wash bedding or other fabrics where pets frequent, every couple of days. This insures that you not only remove the flea eggs, but the larvae and adults.
When you vacuum, you need to change the bags every 2-3 days. Flea collars, flea powder, etc. in vac bags do not work. If you have a bagless you should empty the container out into an airtight bag or bucket of water (let it stand for 15 minutes and discard or flush contents if you're sure it won't clog anything).
Flea adults are prolific little pests and drop round, smooth eggs that typically hatch in carpeting, bedding and clothing - where the larvae can find a meal of skin flakes, dander and such. The adults need a blood meal (dog, cat, rodent, human, etc.) to keep on making more.
By following the steps outlined above, you should be able to naturally rid your home and surrounding area of fleas in about a week to ten days. Diligence and persistence are necessary, but isn't it worth it? All natural, the least expensive option with the highest long-term success rate.
If you want to pay for a flea product, the vet prescribed flea treatments are by far the only truly effective methods of immediate care (you can try the costly over the counter brands, but we've never found that they really work). You may as well just pay the higher price and be done with it rather than buying the over-the-counter products over and over.
If you use the vet prescribed treatment, you still need to eradicate them in your home or you'll just be having the pet treated again when the original Rx wears off.
What about all those flea products? http://www.newmanveterinary.com/Fleas.html#FleaControl
(References: Entomology & Nematology Dept., University of Florida; U.S. Dept of Agriculture; U.S. Food and Drug Administration; U.S. Environmental Protection Agency and others)
According to the Department of Entomology & Nematology at the University of Florida and the U.S. Dept of Agriculture:
Washing all clothing in order to rid them of any fleas, larvae or eggs in them; once you bathe or shower - they are gone from your body (they cannot survive long on a human, especially through a 10-15 minute bath or shower).
Your reaction is probably an allergy to flea bites, which is not uncommon. You could try taking an anti-histamine orally, as well as applying an anti-histamine lotion to the areas in order to relieve the symptoms, or see a doctor for a more powerful solution.
In the way of lotions or other products to use on yourself to deter fleas, some people have had success using typical mosquito repellants such as "Off" or the off brand products.
It's not so much the scent that attracts them, but the heat from your body that they sense. The heat from a dog or cat is higher than our typical 98.6 body temp, and they'll prefer that every time. In some university studies, dogs and cats have been used as 'bait' to draw fleas off humans (and it works), just by putting them in the same room.
The daily vacuuming does remove them as well. You're probably sitting in a fabric chair which is on carpeting - and this is where they are hitching a ride on and meal from you (they need a blood meal to reproduce). Focusing the vacuuming on these areas, as well as attention to daily laundering of clothing and 10-15 minutes baths/showers, should keep them off you. The anti-histamine tabs and lotions should relieve the reaction.