The other day I received a very disturbing message on Instagram, this has happened a few times before but this time I was really scared. I’m thinking about closing my account, but on the other hand, I need to be active for my work. What would you do? Is it possible to fully protect your privacy?
I can say I experienced the same thing. After receiving a message on Instagram, I felt really uncomfortable, so I immediately set my profile to private and closed it off to messages. I recommend that you also set up similar restrictions.
I think if you’re using it for work, you can solve it without completely cutting off your connection to the public. For example, you could turn off story or post comments. Or try creating a new work account and keeping your personal one completely private 
But you’re saying it’s for work, yet on the other hand, you’re getting annoying messages on your public profile. Why are these people finding you? Are you sharing too much revealing or attention-grabbing stuff? Maybe you need to reconsider your profile a bit.
In such situations, it’s important to block disturbing messages immediately and take a screenshot. This is because if the harassment continues, you’ll have evidence. If it escalates further, you can report it as cybercrime.
Let me add that I actually tried to switch to a secret account, but I suspect it could be someone I know who sent a message. That’s why I couldn’t figure out what to do.
Whoever it is, receiving such messages is not your fault. There are those who try to violate women’s boundaries even online. This is never normal, and your behavior should not be excused 
Unfortunately, such things often happen with open accounts. It has personally happened to me 2-3 times; I blocked them immediately, and they neither wrote again nor reached out in any other way. They likely don’t have any serious intentions, it could just be an attempt to scare you.
As a man, I also find it difficult to understand this kind of behavior. Usually, those who send such messages expect a response; they typically give up when you go silent and block them. But if you felt uncomfortable, you should take it seriously.