Butt pain coincide with knee pain?

It is very common for an injury in one part of the body to translate into another part of the body. Knees -> hips/glutes is probably one of the more common. Think about it this way: you have pain in your knee which causes you to alter your stride which then alters the action of everything "uphill". The result is a jacked up (technical term) hip or butt. It is also common for an injury in one leg to affect a muscle group diagonally opposed to the injury. So, when I tore my left calf a few years ago I kept getting alignment problems with my right hip. 

Pain that subsides when you speed up can be a result of poor form at slower speeds. I got my VO2 Max tested at the University of Texas a few years ago and the Dr who performed the test said my form looked like crap (technical term) until I got down to the mid-7's. Once I got going faster I hit my stride and ran much more naturally. 

If the pain keeps up go see a sports therapist and look into the Trigger Point massage tools. Use them well and you'll do much better (unpaid endorsement). 

-Joey
www.RocketScienceSports.com 

It could very well be ITB problems, as I've had outside knee pain associated with outside hip pain at the same time, which laid me off from running for about 4 months.  Could also be some sort of sciatica or piriformis syndrome problem too?

My advise on any of these is go see a sports therapist, because if it's ITB, the problem only gets worse the more you run.  The IT band running from your hip to your knee only gets tighter and chafes more with every single run.  I initially lived with the niggling pain for a few months before the problem became chronic and I had real pain running, and then couldn't walk down stairs either.  Catching the problem early can save you lots of time, frustration, and $$$.  Good luck and I hope you find a solution as there are a lot of stretches and treatments out there.  Getting specially made shoe inserts (I have incredibly high arches on my feet) plus transitioning to minimalist shoes cured my problems, but it did take several months, so be patient.