Hi and welcome,
You might consider something like Benign Paroxysmal Positional Vertigo (BPPV) because that can go away on its own in a few weeks and it's also associated with Nystagmus, BPPV is caused by a problem in the inner ear so you could see an ear, nose and throat (ENT) specialist to see if its possibly the issue.
Down beat Nystagmus is associated with other medical conditions as well as demyelinating conditions like MS, i found a list but everything but 'idiopathic' should of been picked up in your test results and or history though so i don't know how helpful these conditions could be, a few alternative ideas though..
"The differential diagnosis of downbeat nystagmus includes
Arnold-Chiari type I malformation
tumors (meningioma, cerebellar hemangioma) at the foramen magnum
drugs (alcohol, lithium, anticonvulsants)
syrinx of the brainstem or upper cervical spinal cord
nutrition (Wernicke encephalopathy, parenteral feeding, magnesium deficiency)
antibodies to glutamic acid decarboxylase
Hope that helps.......JJ