I am feeling it well should only be used if you're trying to talk about exploring something by touch. To feel something well would mean to thorough feel it, in the more active sense of feeling, rather than the purely perceptive sense of feeling.
If there is a question of whether someone has feeling in their hand, we wouldn't use I am feeling it, unless they were using their other hand to explore it by touch. They would say I can feel it, or I have feeling in it. In neither case would they apply well as an adverb to that usage of feel. They might say I can feel it vividly, or I have good feeling in it (not a good feeling, which would mean something else).
Used more generally, well is used as an adverb for doing things to a reasonable standard. That is not its use with feel, as feel is a linking verb - and well is functioning as an adjective. So a person can say I can hear you well, and it means they can hear you clearly. This knife cuts well means the knife is good at cutting things. In that usage, well is functioning as an adverb. So, let us consider:
She sounds well
This is the feel well sense of well, an adjective as complement to a linking verb. You can also say:
She sounds good
Sounds is still a linking verb here, and good is (as usual) an adjective.
She hears well
This is the adverb sense of well, where it is modifying a verb being used intransitively. We know it's an adverb because hear is not a linking verb.
She hears good
This is non-standard grammar, but nonetheless common in some dialects where good is used as an adverb broadly equivalent to well. I wouldn't emulate it, but you should be prepared to come across it, like "I don't hear that good, I'm afraid" if someone is hard of hearing and apologetic about it.
However, there are verbs that can be linking verbs, but can also be action verbs. In those cases, you have to be more careful. Consider:
You sound your horn.
This means to use the horn to produce sound. Then you can have:
You sound your horn well.
It's obvious here that the object of sound is your horn, and well is an adverb - because you know that sound is an action verb because it has an object. But then you might have:
Suddenly, a horn sounded
Here, the horn is the object of the verb to sound. If well were to be used here, it would still be an adverb, though there are complements that might be used with sound as a linking verb, transforming the meaning.
The horn sounded broken
The horn sounds as if it is broken.
Basically, you need to work out whether you need an adverb or adjective when composing, and whether you're reading an adverb or adjective when you are reading. Some words can be used as both, which can create ambiguity. If there's ambiguity, go for the meaning which seems least weird as an assumption.
A horn sounded well beyond the city wall
Now, ideally there would be a comma here. Did the horn sound well, beyond the city wall, or did it sound, well beyond the city wall? However, the comma is not essential, and which meaning is intended will usually be the one that is most sensible - the horn cannot be healthy or unhealthy in normal discourse, so it is clearly sounding well beyond the city wall - an action verb - rather than being a less defined distance away and sounding well - a linking verb.