Yes it's OK to put Vaseline inside your nose however it's not recommended to put Vaseline inside your nose because when you put Vaseline inside your nose you can potentially get sick by Inhaling small particles of petroleum jelly can result in chemical pneumonitis.
However I have put Vaseline inside my nose for years without any bad thing happening to me.
The Vaseline helps to keep my nose moisturized so it prevents my nostrils from drying out and having a nosebleed.
Since I have started putting Vaseline in my nose I haven't had dry nose and I have not had any nosebleeds in the winter.
So yes it's safe to put Vaseline inside your nose but don't put too much Vaseline in your nose as that could be harmful.
But just a bit of Vaseline in your nose is OK.