I think pretty much everyone has had that feeling, but it will go away in a few days. My suggestion is to drive to a town well away from where you usually hang out, where you know you won't bump into anyone you know and you can completely relax. Then go out and talk to people. Wander around the shops, talk to the shop assistants, go into a pub and chat to the barman. Get used to the fact that people are not looking at your hair - what they are seeing is a normal bloke with a regular appearance - nothing to see here.
Are you aiming to make a stealth transition, without anyone picking up on it? Is that the source of the anxiety? If so, then prepare for the worst - work out what you will say if anyone pics up on the new hair. Hopefully they won't, but you will feel better if you have planned and rehearsed for it. There are a range of options, but my favourite if anyone spots anything and raises it is to say 'yeah, I was thinning a bit, so I have had some treatments to thicken up my hair. But listen, it's still a sensitive subject with me, so if you don't mind I don't want to talk about it, and I would appreciate it if you keep what I have just told you to yourself'. I have used that line a few times when I have chosen to tell girlfriends. If you are really firm and direct like that 99 times out of 100 people will respect your wishes.
Good luck man, and take it easy.
Noah