The most straightforward is
Which indicates that someone is protective more than they should be. Usually used with parents. A mother can be called "overprotective" of her child, if she constantly hovers over them and never allows them to make a mistake or come to any harm, even if they might learn from the experience.
Also works, used for romantic partners, someone is "possessive" of their partner when they refuse to let them spend time with friends, monitor their activities, and allow them very little freedom.
Modern usages aside, if you felt as though someone were acting like they were your father, telling you what to do and running your life, even if for your benefit, but in kind of a commanding, domineering way, you could say they were being "patriarchal". Technically if it were a woman you would say "matriarchal", but it really doesn't have the same connotations. I would probably avoid this one if you don't want to engage in debates over gender politics.
"Patriarchal" can be used to describe dictators, rulers, and kings who treat their subjects as their "family". My understanding is that this was a positive descriptor in Roman times (the word is Latin), but modern people would hate to be called a "patriarch".
Sheepdog, guard dog, rabid dog
If you felt someone was protecting you in a way that was overly violent, you could use one of these. If you had an older brother who hospitalized the neighborhood bully for taking your baseball, you could say he was acting like a "rabid dog". He was protecting you, but obviously in an excessive way.
If your brother followed you around, making sure you never got into trouble you could say he was "sheepdogging" you, although that may be AmE slang that doesn't travel well. It refers to herding dogs that watch over the herd of sheep.