The reflexive pronouns (the ones that end in -self) can only be used when the person or thing they refer to is the same as the subject in the sentence.
In your sentence, the subject is my tummy. The 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 was not you as a person, but the tummy that 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, but itself:
I am so hungry it feels like my tummy is eating itself.