What exactly is your issuewissue with the banned Facebook or YouTube account? It would be easier for us to come up with proper response only if your question is quite legible and understandable. Please provide some additional details to make it more easy for us to grasp your issues.
If your office/ school/college has banned the use of these sites, then you can opt for Proxy servers, or VPN services to access the same. If you are banned by the concerned sites itself, communicate with them on the exact reason for the ban. As a matter of fact, such bans are generally not considered for revoke except in the case certain special cases. You may need to create a new account.
Live....and Let Live!