Hey
In this case I'd say I was furious because the shopkeeper refused to EXCHANGE my T-shirt.
We use exchange when we're making reference to giving something and receiving something back reciprocally.
WE use change we make reference to altering or modifying something.
Take a look:
I exchanged my T-shirt.
I changed my T-shirt.
In the first case it's clear that you went to the store and had your T-shirt replaced with another one for whatever reason.
In the second case, it gives us the clear idea that you had a T-shirt on, took it off, and put on another one.