You need to be seen by a specialist who deals with the spine and the nerves.
You most probably will need an MRI of your cervical spine and your brain.
I would not delay doing so.
Wow, I have to say, "I feel your pain"... literally! I have the EXACT same issue going on with the right side of my body. I have many of the same problems you're having except for the depth perception. Though, I've noticed that I seem to bump into things more than usual, so I wonder if it is off and I just haven't realized it. The only other thing I haven't had is severe pressure in my skull. I've had considerable headaches and occasional tingling in my scalp from time to time. Also, I've noticed the muscles in my neck, back and shoulder tend to get sore with little physical effort and there seems to be a little bit more weakness on that side (that's my dominant side too). I've been going through this for two years. I'm hoping it's a pinched nerve, but my mind races wondering if it could be a tumor putting pressure on a nerve in my head or spine somewhere, or MS, or some other life changing trauma. I also have dizziness from time to time, but I've attributed that to the fluid in my ears. I've also had the tingling in the arms and legs and noticed that over the past couple of years that it's getting more frequent. My only solace is found in the fact these things seem to subside and completely disappear for periods of time. I hope you can figure out what is plaguing you because I've had a few doctors tell me an MRI is in order. My biggest fear with an MRI is the contrast dye used and the links to NSF with people who have had it injected. Best of luck!
Khryce