Who cares if someone doesn’t like that you use iPhone?  I use the iPhone 14 Pro and actually just upgraded to it about a month ago from the iPhone 11.  Been Apple for much of my adult life.  Still am and I’m not planning to change anytime soon.

As for upgrading, your 13 seems like it has quite a few battle scars.  It’s not necessarily a bad thing.  It’s more if the issues cause you problems.  I assume you don’t have AppleCare.  Apple does like to make it so not carrying AppleCare means you have to pay exorbitant rates to get your device fixed.  Also they’re pretty well against right to repair so they make it financially painful for people not to buy AppleCare.  It’s not a perfect situation.  Anyway, does the 16 offer you something you want that is not available to you now?
What about upgrading to a 15?  You’ll have to run the cost benefit analysis for your situation to see if it makes sense.  There’s plenty of value to be realized in used devices so don’t discount it.  For instance, I bought this IPhone 14 Pro and it came with AppleCare.  Now I don’t have to worry that it has scratches on the screen or whatever.  Apple will replace it if needed.