Hi Yurii Both sentences essentially mean the same thing and are natural to use. "I feel good" is simple present tense. It can be labelled as a fact in this moment. "I'm feeling good" is present progressive tense. It implies that this is happening now or an ongoing action in the present, and could possibly continue into the future.

Actually it should be, I feel well, or I’m feeling well. Good is an adjective. The boy is good. The food is good.  God is good.