I don't have a say in this at all, but I just wanted to make you aware of this. Thats not how bans work in the server. Bans on the Gmod servers aren't by IP. Since you (most likely) had that previous account banned, it wouldn't ban your IP, and it would only ban you Steam ID. No 2 public IPv4 addresses will be the same, especially if you are paying for a hotspot that isn't provided by your ISP. So, all together, this is impossible to occur if you haven't closed your current modem and/or router with your ISP.
--TL;DR--
Bans don't go through IP address, and a hotspot will not have someone else's IPv4 address making this impossible to happen.