@jmb73 the test you describe (laying on a table with goggles) is for BPPV which is postural. The eye movements are nystagmus. This means the crystals in your ears got dislodged. There are exercises for this that a PT can teach you and then you can do at home. The Epley maneuver and others are online if you are curious but have a professional teach you first.

Not sure why your doc gave you meclizine or other medicines. Maybe you have more than one cause for vertigo. Labyrinthitis or vestibular neuritis but most people then don't have the nystagmus in that test.