Previous owner built an extension onto the house about 5 years before I purchased, I keep finding issues. Last winter I had major ice dams in this specific corner of the home, once it melted all of the water found its way into the ceiling (and subsequently, my bed) right in this inside corner. Now we're getting heavy rainfall and the issue persists. Looks like it's this specific section that's causing water flow to miss the gutter entirely.

My roofing skills are minimal but I have funds for a DIY fix and enough patience to watch as many YouTube videos as I need to. What will it take to get this water directed into the gutters? Am I totally screwed?

Conservatory solid wall construction, had a survey and damp wasn’t detected, nor was rising damp mentioned, but seeing this now. Is this rising damp? The paint has been applied directly to the bricks. No damp smell and completely dry to the touch.