I'm feeling sick sometimes means I’m feeling nauseatedI'm sick means I'm unwell.If you were feeling faint, you'd say "I'm feeling faint", not "I'm faint".Then there are cases where you have to use "feeling" because otherwise your sentence wouldn't be true. eg. You win $20 in the lotto.I'm feeling rich!  Not I’m rich (which you aren't).

You are sounding tired. You sound tired