How can I prevent collars from curling up

Try this idea:

Hi Gladys, Here's a video that may help: https://www.youtube.com/watch?v=i-mMAbZqmhU

Good luck!

This sounds old fashioned, but I iron almost everything I wear.

Use spray starch and iron.

Yes. You can use spray starch just about anyplace. As an example - I have a pair of jeans that won't hold a crease - so I use spray starch along the fold when I iron them.