My grandma says "Igen akarok sört" should have worked.. is that correct?
Yes, that's correct. It's the literal translation.
Using "kérek" is a more polite and more common way to ask for something.
Haven't we been taught that sör is same as sört?
Sört is in accusative, as it's the direct object of the sentence. Sör is in nominative, you would use it as subject: "A sör finom." -- "Beer is tasty."