Can Twitter block your IP address?

Basically, any social media that detects unusual behavior from you can block your IP address and permanently or temporarily suspend your account.

If you want to hide your IP address, you can use a proxy server to solve your problem. If you use a free proxy server, you can find lists of proxies-- although these lists often contain outdated information showing that the old proxy server is no longer working in the few "good" proxies. Also, because free proxy servers don't make money from the people who use them, it has long been suspected that they profit from your data while you broker. Therefore, if you are trying to hide your IP, a dedicated proxy server is the best choice.

Roxlabs offers a proxy server that can be tried for free and has the most private residential proxies  available.