Oh man xD I had sort of the same problem when i first cosplayed. The first time i ever cosplayed in a public place was when i went to the second Death note live-action movie in theatres as L. I got a couple of awkward looks by people in the parking lot and the snack stand, but so far so good. Then when i got into the theatre, everyone was like "Hi L!" in hushed voices xD Then i sat down with a group of cosplayers there and i had a blast.
Cosplay meetups have been my greatest source of finding friends and people to hang out with. Heck, i met the girl that ended up becoming my first real best friend at the first cosplay meetup i had ever been to last year. Plus, cosplay meetups are great for photos, exercise, getting out of the house and seeing new people, and most of all having a ton of random and crazy fun ^^
So far, i've never been called names or teased for cosplaying, but if anyone does to you, just ignore them :| Judging people by what they wear, no matter how silly or "different" it is, is something that they teach you not to do in pre school. To put it simply: It's just rude.
And if anyone says you don't look like the character, screw that, you know what? You ARN'T the character. I've cosplayed as so many characters that i look nothing like before and i still had a great time cosplaying as those characters because i really liked them. There arn't going to be many people in this world with the face or body of some sexy blonde god/goddess from some romance manga. It's not possible.
And if anyone says your cosplay is wrong or innacurate because you're missing a piece of it or the color is slightly off, just ignore that. It's not the easiest thing in the world to get fabrics that perfectly match up to the colors of the character's outfit, so it shouldn't be a big deal. And sometimes it's hard to find pieces of a costume, such as a prop or something attached to the main costume. As long as people are able to look at the ourfit you're wearing and be able to say "Oh! That's [insert character's name here]!", you shouldn't have any problems.
Anyways, good luck with cosplaying for the first time and i can't wait to meet you at the mall meetup this Sunday ^^