Twitter is making me follow random people. After two days of unfollowing them I get another dozens of people in my follow list. Did my account get hacked or something?
It seems the possibility you have been hacked is quite high. As the Twitter Help Center Page states, here are some common things that happen when you are hacked:
The Twitter Support page states that you should perform the following steps to remedy the issue:
Along with doing this I suggest scanning your computer for malware using a program such as Malwarebytes.