Minecraft too many logins / blacklisted IP help?

I would assume you're on a shared IP network (like a School/College/Work network) or even a small network (siblings sharing the same IP) and multiple users have triggered an internal ban to the network.

If that's the case, you'll need to ensure all users do not make a login request for the next 4 hours, or if you can't control access via all users, speak to Customer Support to advise them that this is a Shared IP. Most online service providers are able to verify the mac addresses and IP address and make it exempt from this type of ban, whilst switching to an alternate method of capturing abuse.