Your paragraph is well-written and already sounds quite natural. I would suggest deleting the word "but" from "but she is also my unconditional supporter." Normally, when we say "not only X, ... also Y," we either use "but" OR we repeat the subject of the sentence -- not both. For example, we would say either: "He's not only smart, BUT also brave." or "He's not only smart, HE'S also brave." It sounds a bit unnatural to say "He's not only smart, BUT HE'S also brave." Everything else looks good! The last sentence is perhaps a little strange because it says she's "warm and sweet, like a river." Rivers aren't usually described as "warm" or "sweet," so the comparison seems a bit confusing. The grammar is fine, though. :)

My mother makes me feel loved and happy. (Her being a person is obvious and doesn’t need to be said.) She takes care of me and worries about me every day, and is also a source of unconditional support and encouragement. (Smoother.) Her love is … (I agree with Gray that Westerners don’t think of rivers as warm and sweet. So the statement conveys that you think differently about rivers than we do. If that’s deliberate, then it’s fine. )

Hi! Great work Hung! Your 'inversion' is almost perfect. We're just missing the auxiliary verb do. "Not only does she take care of me and worry about me every day, but she supports me unconditionaly and is a source of encouragement in every step I take." Very well written Hung! I see you're from Vietnam! I lived there for two years and I miss it so much! Especially bún cha!