Am I allowed to own shares in other companies?

Yes, you are, but you are expected to act in good faith in representing your employer's interests.You are expected to be honest in your dealings on behalf of your employer and not profit from your position or from information that you personally have access to or are aware of as a result of your job.

Having shares in other companies would really only present problems if it led to a conflict of interest and you did not put your employer's interests first at all times, because of personal financial gain.