Water Flow Slow to Start

I have a GE fridge where the water dispenser is on the left side indoor wall, and the filter turns into place at the back top right corner. In the last month or so, it suddenly takes like a full minute of holding the button down for the water to come out into the glass. When I tried replacing the filter, water exploded everywhere, which makes me think the problem is somehow with the spot where the filter turns into its lock position at the back of the fridge. Once the water makes its way into the glass it's a consistent flow, but it's taking longer and longer for the water to start coming out. I switched the filter twice and it keeps happening. Any ideas? Thanks!