I do not recommend the use of antiphlogistin while breastfeeding, no.
Instead, I recommend the use of a cream that goes by the name of Voltaren Emulgel™ (you can find it behind the pharmacy counter, but not prescribed).
Use a small amount on the neck while you receive a massage twice a day.
Also, try to see if those aches and pains could be caused by poor positioning while breastfeeding (this is common) by asking your spouse to look at you for a bit while you're nursing. For example, focus on lowering your trapezius muscles when you're breastfeeding.