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Again this is a very rare situation.
Acupuncture should never be done on an area where there is a rash, vesicle (fluid under the skin), or an open wound. In summary, a needle should never be inserted in an area where skin/tissue is compromised or has an infection already.
Needles can be placed in other areas of the body where there is not a risk of creating an infection from a rash or open wound.
Acupuncture should never cause a bacterial infection if proper technique is being used.
Usually, we put needle at the distal points and yet help the most.
Having an open wound isn't a contraindication for treatment, but the area should be avoided. If you are an immunocompromised patient it would be advisable to wait for treatment to take all precautions necessary, but in a healthy individual risk of infection is still extremely low.
In California by law only disposable needles can be administrated. If proper procedure is followed, there will be close to impossible to have any infection. It is the same risk like a medical doctor administrating a shot. In California, up to today, there's no record of infection caused by acupuncture therapy.
As for the cut on the palm of your hand, acupuncture poses no risk to worsening your condition. Because the skin is open, we would not apply treatment in that area.
Glenn R. Williams, D.C., L.Ac.
If it's still a concern due to the cut on your palm, try to find someone who practices a distal form of acupuncture. These practitioners can treat your hand pain without putting needles in your hand. I know, to most folks it sounds weird, but this is the form of acupuncture that I practice and, particularly for pain, it's very effective.
The acupuncture treatment itself will not bring a bacterial infection to your hand anymore than brushing your teeth would. That is, as long as you didn't brush your teeth then brush your cut with the same toothbrush. A licensed practitioner would again, not needle into an open wound.
Licensed Acupuncturists (L.Ac.s) use single-use, pre-sterilized needles when working on patients. They also do not needle or directly handle open wounds on individuals. In my 20+ years of practice, no one has gotten an infection from my work.
Your wound can get infections from any place if it is not cleaned and covered/bandaged. I am assuming that you are keeping your cut covered with a breathable bandage and are making sure that you don't handle dirty or contaminated items with that hand. These same precautions of keeping it clean and covered should be done anywhere you go.