How do I prevent another iPhone user from viewing my messages?

I’m guessing you don’t mean that they are literally looking at your phone, in which case the advice would be…don’t let them!

Are you sharing an Apple ID with this person? In which case - don’t. They are not meant to be shared. You should each have your own.

Keep the iPhone updated to the latest iOS always and never Jailbreak. That's it.

iOS / iPadOS devices cannot be hacked or infected with Virus / Malware / Spyware if it is updated to the latest iOS/iPadOS unless you have intentionally downloaded spurious software or unauthorized apps directly from the internet and installed on your device or/and have Jail Broken. 

It (Hacking) also depends on how careful are you in sharing sensitive and valuable information pertaining to your iPhone such as Passcode, Password etc with your friends and family members.

Be careful when sharing the device's sensitive and valuable information with friends and family members.

Thumb Rules:

1. Enable  Guided Access before handing over an iPhone to kids
2. Don't share Apple IDs
3. Don't Jail Break
4. Don't share sensitive information pertaining to your device and payment methods
5. Beware of Phishing