Is it true what I heard that watching tv and movies is a sin overall? What about watching sports?

The content is what is important. It's true that many, today probably most, television and movie programs are very problematic, especially because of violence and sex, which are promoting 2 of the 3 cardinal sins! On the other hand, if a program is clean and especially if it has a positive message, or historical documentary, it can even be positive. Some rabbis prefer to simplify things and simply say it's all bad (which is what you probably heard), but the Torah believes in intellectual honesty (not to exaggerate prohibitions) and also, every invention God revealed to man, is meant to be used for good. Watching sports is surely better than most tv and movies, for it isn't based on sex and violence (just don't watch the cheerleaders!). Although it's surely better to spend your time learning Torah, spending quality time with your children, spouse or parent, volunteering or readying a clean book, but there are a lot worse things people do, to relax during their spare time, and surely it's not a sin. One should also be careful not to "over-do" it and go crazy over your team, which can often be immature and extremely time-consuming at the expense of mitzvot and more important things, and may even lead (even adults!) to argue with others about which team is better, cursing players who caused your team to lose etc. It's also definitely better to actively play sports, do exercise and stay healthy, rather than watch other do so!