Choose a room with dust-free air. Gravity removes dust from still air. Filters remove dust from moving air. Probably not the same location where you had the Dremel tool...

Use cotton balls, rubbing alcohol, or similar to thoroughly clean all dust and deposits from a 2' x 2' sealed/smooth work surface

Clean the cavity of the camera with alcohol and a fresh Q-tip and place it upside down to dry.

Open the new lens and clean the inside with alcohol and a fresh Q-tip and place it upside down to dry.

If the Q-tip is depositing any lint, then open a packaged lint-free lens wipe and clean the camera sensor window and inside the new lens.