Q: My son updated his phone today to iOS 9 and now we are both getting each other's iMessages. Any suggestions how to fix this?

You are sharing an Apple ID. One way to get around this is to create an Apple ID for your son and use Fanily Sharing for purchases.

Set up Family Sharing - Apple Support

The short term or easy fix is to go to Settings>Messages>Send & Receive at>You can be reached by iMessages at. Make sure that he is not using your Apple ID or iPhone number as his contact at address.

I have a similar problem. We both updated to iOS9 yesterday.  When I send a text to my son he is also getting the same text show up on his number.  We share the same Apple ID.

Make sure that you don't both have the same phone number checked in the contact address in the You can be reached by iMessages at setting.

I will contact my son to see if that is a problem. I think also having the same Apple ID is causing a problem.  If I had known this would be suck a headache I would have not updated yet.  So many little problems happening.  Thanks for the reply I appreciate it.

That worked so far but I will get him to get his own Apple ID.  Bless you!!