There are quite a number of nouns (as choster's answer indicates) which can be used with have without a determiner. To say that we have {such a noun} refers to an item on your schedule, an obligation, a prior commitment.
But I don't think the meaning is "experiencing something" (as in I have a headache).
I cannot meet you after school, I have soccer.
I cannot join you for brunch, I have church.
I cannot join you for dinner, I have choir.
I cannot join you on the camping trip, I have community service that weekend.
I cannot join you on your trip to the beach, I have school.
I cannot make it, I have rehearsal.
The listener understands from the locution that what follows have refers to an obligation, a prior commitment, often a regularly scheduled one.
Sorry, I have court.
Sorry, I have rounds.
Sorry, I have kitchen detail.
You could even say:
Sorry, I cannot join you. I have Mary.
and the listener would understand you to mean that you had some obligation or commitment involving Mary.
This meaning of have also accepts an infinitive clause as its complement:
Sorry, I have to go.