I know that if I was on the receiving end of what I'm about to say, I'd probably be a bit annoyed at first, but please bear with me.
I think the key question is; Do you need to complain about him, or do you need to find a way to handle him? If you make a complaint, you tend to be seen as a moaner making life difficult, if you can change your approach so that it looks like you've identified a problem but struggling to find a solution then people, HR, your boss etc will be more willing to find a way of helping sort it out. Complaints are really hard for them to deal with without everyone getting really upset.
I'm speaking from experience, I've been working for my boss for over a year now and find it very, very, very hard work, we seem to have a lot in common and want the same goals, we just choose very different paths to get there and that has caused a lot of clashes and my stress levels have escalated out of control (lots of illness, return of depression etc as well as daily feeling sick about going to work) so I decided I couldn't go on anymore - if HR couldn't fix it, I'd have to leave, and as I'm currently ttc and due to current job conditions, didn't really want to take that path - so threw myself into the hands of our new HR manager.
Because she's adopted the view that we are both individuals with our own ways of doing things, we've been able to talk openly to each other about what each other does that upsets each other (with HR mediating as it would never have worked otherwise) and make some 'rules' for us to work by.
It helped me to realise some of the triggers that I was doing that annoyed her as well as vice versa.
I'm not for one minute suggesting that you are doing anything to cause this behaviour, and its certainly not anyones fault - but sometimes two people just don't rub along easily and the only course of action is to acknowledge it, discuss it and work out a plan that you can both stick to.
I don't know if this can be of any help, but at the very least, let you know I know how hard and horrible and scary it is, especially the being worried about saying anything bit.
I also think my scenario has been exceptionally well handled by the new hr boss and without her, it simply wouldn't have been possible.
I hope things work out for you, good luck.