I would say an easy way to keep the differences between the two in mind is to remember that "auxiliary" is a word common in non-medical terminology and generally means the same thing as "supplemental" even outside of a medical context, while "axillary" is specific to the axila, which is the medical term for armpit.
dysphagia: difficulty in swallowing dysphasia: a partial or complete impairment of the ability to communicate resulting from brain injury
It may be difficult to keep these two words distinct from one another, but "-phagia" means "swallowing, eating" in medical terminology. Conversely, "-phasia" means "speech disorder."
lipoma: a fatty lump, usually found between