Another vote here for joining a choir or singing group of some kind. If there is such a thing in your area go for a non-performing choir where the emphasis is on enjoyment rather than practicing for public perfomances. Likewise, if there are singing workshops around, go for them.

The leader of the choir I'm in said that one of the most frequent discussions on choir leader forums is how to overcome choir members' doubts about whether they're hitting the right notes or not.

There is a Catch 22 situation - if you're not confident you sing quietly or hesitantly and that affects your ability. Go in confidently and you usually get it.

While singing teachers can do a lot of good I think that sometimes in a one-on-one situation the focus puts the student under pressure. In a group situation there is less pressure. At a workshop I attended a psychologist friend running it said "Give everybody permission to make whatever sound they like. Give yourself the same permission." In a non-threatening environment like that you can relax and experiment.

Don't expect changes immediately. For me it took a choir meeting once a week for a year and plenty of encouragement before suddenly I felt "hey, I can do this OK". From comments in other threads about the learning process I think learning music actually requires establishing new neural pathways.   

When you sing, if other people stick their fingers in their ears and run screaming from the room seek another opinion. Otherwise, stick with it. It can be fun, satisfying and give many health benefits.