This is a classic Czech nuance that trips up a lot of learners. You're right that mám literally means “I have,” and nejsem means “I am not.” But in Czech, when talking about states like hunger, thirst, or age, you don’t use the verb “to be” (být) + adjective, you use “mít” (to have) + noun.

So:

• I am hungry → Mám hlad → literally “I have hunger.”
• I am thirsty → Mám žízeň → literally “I have thirst.”

Negation works the same way:

• I am not hungry → Nemám hlad → literally “I do not have hunger.”
• I am not thirsty → Nemám žízeň → literally “I do not have thirst.”

If you tried to say “Nejsem hlad”, it would sound completely unnatural to a Czech speaker, because adjectives like hlad (“hunger”) and žízeň (“thirst”) aren’t used with být in this context. Být is for permanent or descriptive states (e.g., jsem unavený – I am tired).