A problem will be using moxibustion which is the use of warming up the body with a product obtained from mugwort plant. But by inform the acupuncturist by your conditions, she will know what she can't use in your case.
Acupuncture can be containdicated if are taking blood thinners.
I have had many patients coming with the same fear just to laugh in the end of their own fear. Tell the acupuncturist about your concern and give the treatment a try. You can always stop if it is not comfortable.
Also look for acupuncturists who combine other modalities of treatment such as tuning forks or craniosacral therapy ( they will use less needles this way).
Loosing weight is not an easy thing to do and it will require a combination of things: diet, physical activity, life style discipline and keeping your body in balance (with acupuncture).
Maybe the root cause of the symptoms have not been completely treated, your body has not got into balance, or maybe there are other things which you need to take into consideration, like lifestyle or emotional life.
It is also recommended that you continue care even after the symptoms disappear. You should go for a an energy check up or reboost at least once a season (there are changes in the body caused by the change of season), the treatment will not only prevent your POCD but will help you maintain a good health.
I suggest you go back to your acupuncturist and discuss the situation and find what is the best approach for you.
In treating the headaches with acupuncture, the practitioner will not only consider the symptoms but mostly will look to treat the root cause of the symptoms. From the Chinese medicine point of view, headaches can be caused by too much liver energy, or too much heat in the body, not enough energy, low kidney energy, accumulation of phlem, emotional imbalance etc. Treating the underlying imbalance will take care of the symptoms. Also the acupuncture treatments aim to clear any blockages in the flow of energy and to balance all the organs and balance the system at all levels body/mind/spirit. Last but not the least, acupuncture is a natural method, stimulating the body's inner mechanisms of healing.