Could be that OP's Reddit username was similar to his Nicehash username, and they were somehow able to track his IP down from there.

VPN or Socks5 proxy's always an option if you want to continue mining at Nicehash in the future. There are a few sellers in the Digital Goods section selling accounts for pretty cheap IIRC if you're looking for a VPN. IP bans really aren't that bad (VPN shouldn't affect mining performance much), but it's still shitty that Nicehash decided to ban you off something that minor.