Not quite... alexithymia is being unable to put words to feelings. It's in the word... a- is not, lex- is words, thymia is feeling. Lacking words for emotions is not the same as not feeling the emotions.
Alexithymia is a common experience, but especially common when other communication barriers exist.
Shows that those psych-whatever-ists knew drat about the (ancient) greek language, because 'word' would be 'logos' and 'alexi' is actually a greek surname of ancient decent, that would mean 'defender'. The ancient greeks would never have named the condition that way! My impression is that various Freudians and Anti-Freudians converged on the term in the early-mid-20th century as a means to make themselves sound smarter than any of them really were.
Source: As someone named Alexander, I just finally felt vaguely offended enough by the term to start digging a little deeper:
And also, nothing about the condition as described by modern sources ever made any sense to me - which after reading the article I linked, wasn't even a surprise to me anymore. Sorry, rant over.
TL,DR: It's another piece of etymologic fallout from a historic shitslinging match between researchers and practitioners, but one that didn't get resolved conclusively. Because brains ...