Nobody likes having their life suffocated and that is what you could be doing to your partner. Or maybe that's what your partner is doing to you? It seems harmless enough in the beginning. And could be mistaken for a form of showing how much you love them. You want to be around them every second of the day. Because you don't want to miss a single thing going on in their life. Who they talk to. What they are talking about. Where they are going or have been. They just can't turn around without you being right there beside them. Is this healthy for you? Or them? No.
Everybody needs space. Even if they think they don't. People need to be alone in order to think on their own. If you don't give your partner a little breathing room to think and do things on their own, you are suffocating them. And if it goes on long enough they won't be able to have a thought of their own. The next thing will be that they will be dependant on you for every decision they make in life, to the point that they don't even know what they used to like doing, or what they want to do now. They will only be thinking of what you might want them to do or think. What kind of life is that?
If it is a matter of trust, like you feel like you can't trust them if they are out of your sight, then you would be better off without them. And they would be better off without you. The worse thing you can do to your partner is to not let them have a life of their own. When a person is being suffocated they lose their creativity. They can't become the person that they were meant to be. Relationships should be shared, not controlled. If you don't want your partner to be all they can be then you are trying to control them. And you need to ask yourself why.
If your partner wants to do something or go somewhere without you and you find that this hurts your feelings or makes you mad, then you need to examine your own life. Why does this hurt your feelings? Why does this make you mad? Is it because your jealous? Or is it because you think you can't trust them? Whatever it is that creates these feelings the truth is that they are your feelings. That means that it is your problem.
What to do? Give each other some breathing space. Let each of you have time to think. Then when you are together, share your dreams!