Not much to add, my brothers have given great advice and shared their experiences...I say do it...no more worrying about hair loss and in no time at all, everyone will forget you had hair....I actually enjoyed watching peoples reactions...."what is it....oh wait....I left my toupee at home"! Welcome to the brotherhood
Welcome aboard.
Firstly, you say your hair is falling out? If it is then I would recommend you see a doctor in case something is up. Unless you use the term 'falling out' to mean general hair loss.
Then, shave the dome! You will be amazed at how it feels. But, you have to let yourself get used to it. Give it a good month or so. See if you can live with it. I bet you will love it.