The reflexive pronouns (which end in -self) can only be used when the person or thing they refer to is the same as the subject in the clause where it appears.
In the clause in question here, the subject is my tummy, the verb is is eating, and the problematic pronoun at the end (the object) is me/myself.
If you use a pronoun instead of the noun phrase my tummy, it has to be it: “How is my tummy? It is hungry”. That means it is a pronoun in the third person—not the same as me, which is the first person.
Therefore, you cannot use the reflexive pronoun; it must be:
I am so hungry it feels like my tummy is eating me.
If the object being eaten were not you as a person, but the tummy which is also doing the eating, a reflexive pronoun would be called for—but then it would not be myself, since the tummy is third person; it would have to be itself:
I am so hungry it feels like my tummy is eating itself.