Quartz (Crystals) have a natural vibration to them and some people can be very sensitive to it. I also suggest cleansing your crystals. But you should also work on your chakras as well. If you are getting headaches (sick) then its possible your third eye is too open.
As for the crystals moving? really? can you give more detail on this?
I'd suggest cleansing them and maybe yourself and the house as well if things are moving around. Also if they're moving spots maybe think about why they're in the spot they are or why are they being moved? And as for the making you sick try looking into the properties of the crystal as well, you could just be highly sensitive to it, or you really need the crystal and maybe if you work with it slowly at first the sickness might wear off? Good luck with it :)
Cleansing is a method used to clear out stale, residual or negative energy. Whether it's you, your house, books, work space, spiritual tools like crystals and cauldron, all need regular cleansing. Methods of cleansing and energizing are a plenty. Look them up.
Crystals as well as other items contain different properties so you could be allergic, but not always. If you don't cleanse then they can have backfires because they have a back up of energy which sometimes led to negative results. It might not be the crystals either. It could of been something you ate, worn, or anything of that nature. I know it's sometimes hard for me to wear different types of jewelry and all that because I am allergic to the element Nickel.
Crystals are affected by ones mental and physical being since they affect your energy.Crystals absorb as well as give off energy.A crystal you wear is attuned to you as well as you are to it.Crystals,gems and stones are all worn by a person for its energies to aid you in your daily life.I wear a stone and it would make my hand hurt whenever someone sick was around or I was about to fall victim to a bad situation.
You did not state what type of crystal you wear.According to what you use it for is why its getting you sick maybe its a warning.Also cleaning it can also work wonders.If your crystal has absorbed to much negative energy and you do not clean it the reason you are wearing it would be hampered.
There are many ways to cleanse a crystal:
You can cleanse it by leaving the crystal in a place where it can catch the rays of the sun or moon.You can leave it next to a plant,you can use incense,leave it by a lit candle,etc.
Its not impossible for you to be allergic to it after all a crystal is just an over heated rock made up of many other elements.Maybe something in this crystals make-up is getting you sick.