I can't help but question people who say appearance doesn't matter in the slightest, unless they're the kind of person who's asexual but not aromantic. I'm sure there are underwhelming women and manly, manly men out there with whom I could be a close friend and live in a tiny apartment without hitting my head with a brick, but I can't force myself to sexually function if the spark ain't there. And maybe sex isn't a part of every relationship. That's cool. But damned if it isn't convenient to open the valve with your ring buddy.
And the nice thing about attractiveness is it's super subjective, so don't you worry your unconventional face about it. I for example have been told I have rather unusual taste. Not exclusively or anything, so just because I find you attractive doesn't mean you're an absolute gargoyle, but-- oh man, I'm digging a hole here.