My advice is to keep it from others until you are more comfortable about it yourself.
But, if you're going to get anxious and nervous around people, then they will react to you differently and then this will feed your anxiety.
It becomes a viscous circle.

To break that circle I decided to make my hair the best I possibly could, so that I became proud of what I'd created.
I still didn't tell anybody it was a wig, but I felt so good about the result, I convinced myself no-one would believe me if I told them the truth.
Which is exactly what happened.

I dare say your replacement hair looks a lot better than the concealers did.
So people will notice something is different/better, but they won't know exactly what.
Some will eventually work out its your hair that looks better and when they say so, it can feel awkward because its the last thing you want to talk about.

So be prepared for compliments and learn to accept them for what they are.
Get yourself a stock answer ready like "Thanks, I've found a new barber" or "I'm using a new shampoo". Anything will do, as long as you have it ready to say to get you through the moment.

As time goes on it gets easier and believe it or not, one day you'll even forget you're wearing it at all.