Filter Pressure Increases Rapidly

First off, I am a newbie and I have been reading on this site all morning...I love it! I am unable to search yet so please direct me to any pertinent info. I have a home warranty policy that covers my pool equipment. Several years ago I had my huge stainless steel filter replaced with a smaller Sta-rite S8D110 unit (pool guy said that is all the warranty would cover). A few years later I had the pump replaced with a Champion Waterway 110 1hp pump. I don't remember what hp my previous pump was. I have always battled the pressure in my tank. I've replaced all the grids, o-rings, etc. I've checked for any obstructions in the two-way backwash valve and Jandy valves. My initial pressure after pre-coat is 12 psi. Recently I took all the grids out and individually cleaned them with filter cleaner and pressure washer. After restart, sometimes within 15 minutes the pressure works its way up to 20 psi then ultimately 30 psi after which the o-rings in the two-way valve leak water out the backwash piping. So I did a little research in the technical manuals for both my pump and filter. I discovered that the filter is rated at 106 psi MAX, and that my pump is rated at 120 gpm @ 25ft. My pump is only 15 ft from the pool (not figuring in the underground plumbing). My question is: Is my pump pushing more water than my filter can handle? If so, what can I do about it? How come when I backwash, the filter has no problem moving that much water (0 psi on the gauge)? Forgot to mention my pool is 20 years old, 25,000 gal. in-ground.

Sorry for the lengthy post...I figured the more info I provide, the better the info I receive. Thanks in advance, and once again, I love this site!