Is a few drops of water large enough to cause an infection from naegleria fowleri?

Rare but not impossible. Naeglaria Fowleri is a rare parasitic infection which typically occurs in persons exposed to freshwater under high pressure- the parasite can get access to the the brain through migrating up the nose and cribiform plate. Can occur when free diving in freshwater lakes for instance. It is exceedingly rare but can be fatal.

Naegleria Fowleri is a parasitic infection through the nose caused while swimming or diving in warm freshwater places, like lakes and rivers. Please reference the CDC website: https://www.cdc.gov/parasites/naegleria/general.html