Your horse should not be pushing on you or invading your space. This is where it is good to have a solid foundation on groundwork.
Before you go back to clicker training, take him out to the round pen and walk trot canter him both directions. Ask him to whoa and yield his hindquarters away from you. Put a lead on (if you need it) and ask him to back. Ideally he should back without a lead on.
He should be respectful by the end of the lesson. Now you can start with clicker training the back up. Ask him to back 4 steps, click and reward. It shouldn't take long and he should be moving away from you. If he is touching you/nosing you as you back him, then you aren't doing it right. Raise your hands, shake the lead and say back and walk straight towards him as if you will run into him. You may need a whip if he is really stubborn about backing. If he is respectful he will move out of your way. Repeat it with the clicker 3-4 times and quit for the day.
I do not like to spend more than 5 minutes working on clicker training unless it is something really challenging like Spanish walk or bowing. Maximum of 10 minutes.
Another yielding exercise you can do with the clicker is side-stepping. Again you are asking the horse to move away from you.
I have been run over (and luckily unharmed) too many times to ever tolerate a pushy horse. If he is nosing you, back him up! Get him out of your space. You don't have to beat him or hit him in the nose, but push on him and make him move away from you. I don't care if you ask him to move sideways, back, or just move his head away.
Are you familiar with the porcupine game by parelli? Horse Training Games - the Porcupine Game
I'm not a real big parelli fan, but he does do a good job explaining pressure and release!
Do not reward pushy behavior! If he is all over you, he is being pushy.