Thanks for the info on fences, guys! That's why I love the forum, you can always get good advice, even if you don't start off asking, lol.
I'll try and talk to my mother about the less vet bills, better fencing stuff... I dunno if she will take that, though, as the majority of my horses vet bills have been because we fell while riding, the horse stepped on a nail, or something like that... But I will try. She'll probably just say that it's my grandma's pasture and my uncles responsibility to put up the fence, but it never hurts to give it a try, lol.
I've been caught in the barbed wire before, and so have a few of my 5-13 year old cousins. That's the main reason I dislike it so much... it hurts... and it leaves scars, no matter how small the wound is...
Another update, though... Jax's wound is looking sooo much better! The swelling is all gone now! I'm still putting meds on it twice daily and he's so calm about it... still hosing it out, too... he's getting so much better with water from the hose-pipe... (hopefully I can give him his first bath in the next few weeks!)