私はストレスがたまると食欲がなくなるのではなく、逆に何か食べないと気が済まなくなる。

、。

When I'm stressed, rather than losing my appetite, I actually can't feel settled unless I eat something.

Literal

I [topic-は] stress [subject-が] accumulates [conditional-と] appetite [subject-が] disappears [not-X-but-のではなく], conversely something eat-[unless-ないと] spirit [subject-が] can't-settle.

~のではなく corrects a common assumption: 'it's not that I lose my appetite; rather, the opposite.' 気が済まない (can't feel satisfied/settled) is an idiom — the spirit won't settle down. 逆に (conversely) signals the reversal. ~ないと acts as a conditional: 'unless I eat.'