My understanding is that if the verb "to feel" means "to be" then we use an adverb after it; if it means "to touch" then we use an adjective. But we can't say:
I feel nicely.
Why not? I can't understand it.
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I think you have it backwards.
The verb "to feel" generally means to experience a sensation, either physical "I feel hot" or emotional: "I feel happy." I think that's what you mean by it meaning "to be" - and you'd always use it with an adjective and never with an adverb in that sense.
"To feel" can also mean to experience the sensation of touch, generally by examining something with the hands. You'd use an adverb in that context: "He feels the fruit gently, so as not to bruise it." I think you'd always include an object to be felt, so it would be "I feel OBJECT ADVERB" and not "I feel ADVERB" (though you could probably construct a scenario in which "I feel ADVERB" would be acceptable).
It's also possible to use the verb, in both senses, without adjective or adverb: "She feels her skin prickling," "He feels for the light switch."