Make sure when you make your feature class to NOT give it a projection, or put it in a Geographic Coordinate System. Let it just project as a raw lat/long value and it should be fine, as ArcGIS projects all data on the fly to the projection of the dataframe. Since the data is not projected, it does not need to be given a projection.
I'm guessing the lat/long values came from a GPS or something?
I made some points for around Memphis, TN from raw lat/long and when I brought them in with in NAD83 UTM 15N it put them off the coast of the Galapagos Islands.