Could a cat scan show inflammation of the brain without contrast dye? i had a ct for amoeba and headaches & no dye was given but doc says i'm ok.

Yes: A non-contrast ct scan can shows signs of tissue edema/swelling, which occur with inflammation. If there is true concern for encephalitis, an MRI would be a better test, but likely not warranted given your presentation.

Not the best test.: In severe acute inflammatory processes, ct can detect brain edema, but it's unlikely you would be in a state to be able to recall that much. Assuming you're ok now, it's doubtful you had amebic encephalits, since that is a very nasty disease!