"He said my warranty would not cover it"
Ummm...the OP REALLY needs to learn about what a warranty entails.
A warranty does not cover maintenance costs--regardless of what the odometer mileage factor might be.
A warranty does cover the cost of repairs, however.
The object of good maintenance is to avoid having to repair the car, as those repairs will likely take place after the expiration of the warranty.
Much of the decision about when to change oil--and to do other maintenance procedures--has to do with the elapsed time factor, in addition to the odometer mileage factor.
So, my suggestions for the OP are as follows:
>Read both the actual wording of the warranty, and the manufacturer's Maintenance Schedule.
These are two entirely different entities, and the OP clearly needs to familiarize herself with both.
Tell us how many months the car has been driven in order to accumulate those 6k miles.