It is not "easy" to ruin a horse's tendons by using polo wraps. You would have to wrap it super super SUPER tight every ride for weeks for it to really do any damage. I use my polo wraps all the time, and I've never had a problem with them. If you can put a vet wrap on, you can put a polo wrap on.
That being said, if you're doing serious jumping, I would use a boot, because they do offer more support, but for what you seem to be doing now, you will be fine using polo wraps until you can save up for boots.