How do I make sure someone next to me doesn't read my messages the same time am reading

Do a Google search for "iPhone Privacy Screen Protectors" and you can buy a screen protector that makes it difficult to read the screen unless you're looking directly at the screen.

lorot wrote:

How will I make sure that someone who is next to me is not reading my text

Then don’t sit next to them. On the other hand if your question is really about whether the person in your vicinity can somehow read your texts on their device the answer is a definite NO, they cannot.

Don't show them the screen