I still think learning to drive would be good in the overall scheme of things. What if your child needed medical help or there was some other emergency? What about when your child is older and going to Dr, dentist, school and other appointments? What if you needed to picthem up from school because he was sick or whatever? Are you going to depend on family all your life?
It might take a long time to get over the anxiety about driving but it IS doable. Just take it slow. In small doses. Without your child in the car. There are even driving schools and community driving awareness classes. (Usually for senior citizens, but hey!)
Many people aren't crazy about driving and getting behind the wheel is a daunting responsibility. But so is raising a child, and you're doing that just fine.
Your husband could live without a vehicle one day a week. 20 minutes is NOT that far to drive him (many people live an hour or more from their workplace) and if you ran errands on the way back, wouldn't be that bad. He could pack a lunch too. Many people do that. It isn't fair to you to use those excuses, even if you AREN'T currently driving.
As for meeting people, (not telling you to change who you are, believe me!!) , but do you really think your appearance prevents people from approaching you/feeling comfortable with you? Do you genuinely WANT to hang out with this type of person? It may be that you have to meet people part way. Like, don't wear your most far-out outfit or hairdo the day you're headed to the Mommy group at the mall? Doesn't mean you have to change your life permanently, or all the time you're in public, just adjust things for certain social events and circumstances.
I don't wear a swimsuit (or even my Greatful Dead Tie-dye shirt) to church because I know I would terrify some of the people, even if it's just the little old ladies - heh. Yes, people SHOULD accept us as we are, but it just ain't always true and you just gotta help them out.
So, even though I'm not as crazy about slacks and a nice blouse, I enjoy going to church and meeting people there, so I wear that because it makes me more approachable in "their" territory.
So the town newspaper is small. Maybe they need fillers, like an "ad" for a friend to share playdates. Contact the paper and see if they would post something for you.
Though, again, driving is going to help here as I can't see someone befriending you and then always doing the driving for your playdates too.
Is there a local library? (If the town has a mall, it should have a library) They usually have children's story hours and sometimes even craft times. And they always have bullitin boards. Make a cute colorful poster maybe?
What about a Senior Center. Sometimes they need volunteers, and seniors often (not always) LOVE well behaved small children.
I hear ya though. Ares is getting to an age where it's nice to start having peers to interact with and learn about sharing and communicating with. Keep looking and asking around. Something will turn up!