Can I get a new IP address & is it legal to ask my ISP for one or try to get a new one myself, manually? I'm unsure if twitter blocked/blacklisted my IP address. I didn't break any rules. Only 1 person I follow, who didn't block me, their tweets keep appearing then disappearing on my timeline & every time I contact twitter support, they only send me automated responses with links to resolve my issue.
It's perfectly legal to ask for a new IP address, but it's probably up to your ISP if they want to give it to you. Most ISPs (unless you've specifically asked for a static IP) will refresh your IP every few days. Try restarting your modem and/or router, sometimes that will refresh your IP address.
Since you can access Twitter, it sounds like the problem is more related to something else. Attempt it in a different browser, or, as Cory M suggested, try it from another Internet source - say, a coffee shop, a smartphone, or a proxy.
Yes, it's perfectly legal because your ISP owns the addresses they give you. Mediacom allows you to simply type:
ipconfig /release then wait a few seconds and
ipconfig /renew . I would guess that MOST ISPs will allow this type of standard DHCP requests. The benefit to doing it this way is that you don't have to wait for it to happen. Also, if your ISP is going to allow this then this is how they're probably going to have you do it anyway. If you have a static IP this will not work. That is unlikely however.
I'm purposely ignoring the Twitter part of this post. If you want me to answer something about Twitter you'll need to ask a new question.
You might want to try using Tor, which is an anonymizing proxy network. It will route your traffic through a series of random proxies, effectively changing your IP every time you make a connection (your original IP will never be used).
As with all proxies, you need to be cautious about what you send through Tor, as the end node (the last proxy in the chain which sends your data to its final destination) will be able to read your data unless you use HTTPS or other end-point encryption.
Twitter and most large websites allow you to use HTTPS these days so this shouldn't be much of a problem. Tor even has a modified version of Firefox that should simplify the installation process.