I had this issue with Google Search a few years ago and fixed it.
First the cause: you, a program you have on your network, or some douche neighbour on your IP block (this was my problem), is bombarding Google Search.
Fix is simple 1) either wait it out - once the queries end, Google will unban the IP block or 2) change your IP address.
If you are sure that you and your network are not the cause, then you are most likely sharing an IP with someone else. Usually it's due to a privacy setting from you internet provider. Anonymous IP I think they call it (as opposed to Public IP). Think of it as multiple accounts/households being all routed with one router, so that you are "indistinguishable" from your neighbours. Someone/thing behind that router is bombarding Google Search, and Google Search can't tell the difference between you and that person/thing doing the bombarding (hence why it's called Anonymous IP).
It may also be some weird software that is providing this anonymous ip service. I don't know.
I'm pretty sure Bing will also ban for bombarding Bing Search with automated queries.