dinonline responds to your question as such
The idea of pas shel shacharis — morning bread, or breakfast — is not
an “obligation,” but is stated by the Sages of the Gemara by way of
good advice. The Gemara writes that no less than 83 ailments are
countered by “morning bread,” and a number of additional benefits are
also mentioned, such as the ability to focus well on one’s studies,
and another twelve benefits (Bava Metzia 107b).
The Tur (Orach Chaim 155) mentions the concept of eating breakfast,
and writes that it is a mitzvah to take care of one’s body, and to
ensure that one is strong for the service of Hashem (see also Mishnah
Berurah 155:11, who cites this).
For deeper meaning of the matter, see the Maharal, in his Chiddushei
Agados. See also Yaaros Devash (1:6), who explains that Chazal mean to
teach that one should not search for pleasures, but make one’s custom
to eat bread and water.
Therefore, although it is good practice to eat breakfast, there is no
obligation to do so, and everything depends on personal circumstances.
If you will feel better without eating, you should not eat.