I have worked with stones for over 30 years.   It's not the stone that can cause you to feel sick, it's the stone trying to balance or heal your body that produces a healing crisis.  Sometimes we just need to stick to the plan and work through it.  If you can't and you have a specific symptom, you can find another stone to help with that in the mean time. Sometimes I recommend people use flower essences along with stones if a healing crisis occurs.  Stones in general do not cause things like headaches.  That would put them in the same category as prescription drugs that cause side effects worse then the original disease.  It's best to work with a qualified person if you're interested in working with stones or take some classes.  As with any thing else, it does require some knowledge.
Blessings

I was informed that stones can have negative effects if one does not cleanse them.  I personally have no expierenced the bad effects, because I cleansed them once I got them, but just thought I'd share what I had heard.

Stones do need to be cleansed often.  I have never had stones give negative effects from not cleansing but they do not work as well or work at all if they collect negative energy.  The crystal should be attuned to a specific use after cleansing when you first acquire it.  If a stone is attuned by you to healing then you should stick to that.  If it is used for meditation that it should be used for that.  If anyone has had any negative experiences, I'd like to hear abou them.
Blessings

This stone is useful only if your blood count is low.it will create acidity and vomiting if Haemoglobin is on higher side.
                            Dr jayant kulkarni

Hematite: Mental attunement, memory, calming, balance, grounding, centering, focusing energy and emotions, peace, inner happiness, transforming negativity. Healing lore: keep the body cool, blood disorders, nervous problems, insomnia, align the spine, mend broken bones, anemia.

Hematite Brings peace, self-control, concentration, balance; rids negativity; legal help

Meditative grounding stone brings tranquility and emotional clarity. Assists in dissolution of negativity, transforming it into universal light of love. Can stimulate desire for peace, self-control, and inner happiness. Assists in treatment of leg cramps, blood disorders, nervous disorders and insomnia.