I like Bobbie's rewrite Van. The 'squirrel' rhyme didn't add much to the story and was obviously just there to rhyme. The curl rhyme worked because of the context, as in, 'The girls all get prettier at closing time' because of the debilitation in mens' and womens' 12-ounce-curl-impaired judgment.
This plays like a commercial and might be a good video format, asking the questions setting up to pitch something for sale to solve the problem. In fact I may open a company, Ugly r' Us, and hire ugly folks for wingman services. They're not doing anything on Friday and Saturday night anyway. Might as well make some money.

UGLY FRIEND
Copyright 2005 Van Borden

When you both like THE SAME girl
Does your friend always win?
Does he have cosmetic appeal
That makes you envy HIM?

NEW VERSE II
When you'RE both OUT IN A crowd
Do women check him out?
You CLEAN UP GOOD but THINGS GO BAD
SOON AS YOU LEAVE THE HOUSE.

CHORUS
You need an Ugly Friend
WHO YOU CAN STAND NEXT TO
You need an Ugly Friend
So the GIRLS WILL look at you
YOU'LL HAVE TO TREAT HIM KINDLY
AND HELP HIM BE CONTENT
WITH THE CONSTANT REMINDING
THAT HE'S YOUR UGLY FRIEND.

WHEN YOU GO out girl hunting
DON’T tell your friend the deal
You'll roll off with the girl and leave
Him like a flat third wheel

BRIDGE
Now I know WE ALL NEED FRIENDSHIP
AND friendship SHOULD BE true
But HAVE YOU EVER WONDERED WHY
Your friend hangs around with you?

(REPEAT CHORUS)

There will always be another song to be written. Someone will write it. Why not you? www.garyeandrews.com