Hey there,
If your bank character is below level 15 and you were using public channels, it's likely you were banned by the chat spam detection system.
If you were banned for multiboxing its because you're only allowed to multibox if both characters are in a capital city (banking, trading etc).
Here's the rules from the ToU
Multiboxing refers to playing multiple characters simultaneously. This can either be achieved by using multiple machines to run the Game or by running multiple instances of the Game. The following rules are not meant to be exhaustive, and using multiple characters to level, farm reputation, run dungeons, do raids and/or engage in PVP is considered Multiboxing. Each case of Multiboxing will be judged individually and thoroughly. There are a few specific situations where you may have two characters in-game simultaneously, *only while both characters are in a major city*:
Transferring items between accounts;
Using professions, as long as no farming or material gathering is involved;
Crafting, enchanting, banking and/or for trading purposes that does not include the Auction House.
Portalling a second account only to and from major cities.
Playing simultaneously on both PvP and PvE realms. *Not restricted to major cities*
Best of luck