I get headaches after putting presure on gb20

GB 20 is a commonly used point to alleviate headaches. If someone has true neck issues (herniations, arthritis, any kind of instability) too much or too strong of pressure could exasperate nerve problems in the upper cervical discs leading to headaches or worse... It would generally subside after a few days unless the pressure caused further disc alignment issues. I would assume your physiotherapist knows your case and would know better, however, some people unfortunately view acupressure as a "it can't hurt" type of treatment. Whereas, improperly applied it can.

Acupuncture would not cause/contribute to this problem on GB 20 and should be helpful (along with other points) to alleviate all of your symptoms. The effects of acupuncture vs. acupressure are quite different. In the meantime you can try using acupressure on LI 4 to see if that helps your headache pass.