Final answer:
The swelling of the nail often associated with the thickening condition Onychauxis is known as nail clubbing, which can indicate underlying systemic health issues.
Step-by-step explanation:
The swelling of the nail that is often associated with Onychauxis, which refers to the thickening or overgrowth of the nail, is known as nail clubbing. Onychauxis on its own pertains to the hypertrophy or thickening of the nails without necessarily involving the surrounding tissue. However, nail clubbing is a condition where the nail curve becomes more convex than usual, often accompanied by the softening of the nail bed and swelling of the surrounding tissues, making the base of the nail feel spongy or floating. It can be a sign of various systemic health concerns, including respiratory diseases, cardiovascular diseases, or gastrointestinal disorders.