The well / good thing is always a tricky one because of, as usual, ambiguity.
- good is the adjective
- well is the adverbial form of good
- How are you? (I am) good.
- How are you doing? (I am doing) well.
- Equivalent expressions with different grammatical structures.
- well, though, can also be an adjective meaning ‘not sick’
- and it’s that adjectival form of well that causes all sorts of problems, both because well is an adjective and an adverb and because the meanings of each are similar enough to easily overlap
In this case, the use of well is likely technically correct: feel is a linking verb that takes an adjective after it, the discussion concerns Tiger Woods’ health, the adjective well, meaning ‘not sick’, fits both grammatically and meaning-wise.