My specialist recommended an MRI, not a CT, after a month or so just to rule out any other issues. He said that MRIs are more useful than CTs after several weeks have passed (CTs being potentially more useful in the very early stages).

In most cases, MR scans will be negative (this is good), but sometimes something will show up. If a competent concussion specialist recommends getting one done, I would do it. Getting my results ("unremarkable scan...no evidence of trauma sequelae") brought me some peace of mind.

Note that some MR scanners are more up-to-date (and therefore useful) than others.