Well the definitions in german, which are most probably applicable to english aswell, are dating back to latin. A feeling is something you feel with ur senses, like "this feels cold", "the sun is warm".
An emotion is an evaluation of a feeling, an ex-motion comes from the inner self to the outside and that is for example: "I feel awkward." "I feel cozy"
So in combination you can say: "The tea is hot (feeling), I like that (emotion)". "The lunch is cold (feeling) - that upsets me (emotion)."
The intresting thing in that regards is Jung's definition of J-types being the ones more prone to have a fixed opinion. It's not that there opinion is always an emotion, it can be just an opinion aswell, but according to theory p-types should be less prone to showing emotions. What are your thoughts ?