Feel has several meanings.

to touch something.
– Feel the car seat. It’s wet.
– Progressive tenses are possible.
– ‘ What are you doing?’ I’m feeling the shirts to see if they are dry.’

to receive physical sensations.
– I suddenly felt something on my leg.
– We do not use progressive tenses, but we often use can feel to talk about a present sensation.
– I can feel something biting me!

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to think, have an opinion.
– Progressive tenses are not used.
– I feel that you’re making a mistake. (NOT I’m feeling . . .)

Copula verb, used with adjectives.
– Your hands feel cold on my skin. I feel fine. Do you feel happy? Progressive forms can be used to talk about one’s ‘inside’ feelings.
– I’m feeling fine. How are you feeling ?