Each user connection has a specific mask/ip, like [/b]muskateer@somthing.here.com,you can see yours by typing in mIRC /whois muskateer (or whatever your nick is)
A ban may not have been set on you specifically, but on a range that includes you. For example, if i set a ban on *!*@dumdum.here.com, you wouldnt be effected, but if i set one as *!*@*.here.com then both you (something.here.com) and dumdum.here.com would be effected. The * is a wild card, which means it doesnt care whats in that space, it will grab everything with here.com. The same thing would apply to a numeric, like [b]stuff@123.456.123.456.
I would suggest checking to see what your mask is with the wireless, then with the dialup and ask one of the ops in that channel if the ban could be narrowed so you arent effected.