My son’s number is receiving my texts. We are on the same plan.

Like SranvanKrA is saying separate your accounts. You can create an account for your child on their device there are a few Apple Support articles for this exact situation. If you create an account for them your Messages should be separate. Additionally as a bonus you can manage their account through Screen Time and Family Sharing to protect and safeguard them online.

Probably you both are using the same Apple ID.

Use separate Apple ID. Alternatively,

Disable text message forwarding

1. On your iPhone, go to Settings > Messages > Text Message Forwarding.
2. 
3. Disable the devices which is reading your texts
4. 

Worth a try, but no guarantees.

On your phone.......

Tap Settings

Tap Messages

Tap Send & Receive

The only check mark should be next to your phone number

On your son's phone.....

Tap Settings

Tap Messages

Tap Send & Receive

The only check mark should be next to your son's phone number