Is $300 to repair a small section of roof with new drip edge and soffit a fair price?

Water is flowing behind the gutter in a small section of my roof, and the wood is damaged. It's currently raining, and water is still getting behind the gutter. I'm wary of cheap work and unsure if the proposed solution of replacing the drip edge will be effective since there's already one there. I'm trying to get this done as soon as possible because I'm also working on a 300 sqft sunken patio and want to enjoy my pool. I don't know much about roofing and am concerned about potential long-term issues like rotted rafters or raccoons in the attic. I plan to add a soffit vent in this location if possible, as I have them elsewhere.