Using a proxy without the permission of the owner is not legal in most places. Most networks also disapprove of it and will ban you for using them if detected.
If a network or room owner has banned you then you have no right to circumvent the ban in any way. It does not matter if you have done something wrong or not. Connecting to IRC means connecting to a computer owned by someone else and the issue of who may connect lies solely with the owner and their appointed staff (if any). Personally, when I see someone evade a ban I place, regardless of what they think their rights are my usual response is a stronger ban, EG: their domain, a z:line on a vhost provider's c class, even a TLD if necessary.
Your only resolve is to use another server or network until the ban is lifted.