The part you're referring to are called guard liners and they're made of swiss cheese unfortunately
Best bet would be to remove tyres and re-secure them into the existing holes or create new ones (if you're not confident drilling holes into your car then yes take it to a tyre shop/panel beater).
I think replacement liners are around $90 each? but before doing anything take the tyre off and see if the plastic fasteners are still there or if they have simply been rubbed away due to as you've said above)
Without seeing the extent I would suggest having a look underneath and see if the liners are still attached to the bumber.
Plastic also expands and contracts 'which unfortunately leads to stretching', have you tried either re-tucking them back in or modifying them to fit better?