The difference for these two is very subtle. For most expressions, you can use either "I feel" or "I'm feeling" and they mean the same thing. They are both present tense. Often a verb that ends in "-ing" can emphasize that the action is taking place RIGHT NOW. But most English speakers use "I feel" and "I'm feeling" interchangeably. One of the confusing parts of learning English, I know! :-)

Native English speakers use both expressions mostly interchangeably. Note that in spoken English, "feel" is often used to mean "believe": "I feel that you're not telling me the truth." Many English speakers "feel" that this definition is incorrect, but some dictionaries actually show it as a lesser-used definition.

"I'm feeling" -- грамматически неправильно поскольку глагол состояния