Other users reported that some kind of animation overhaul/addition mod was the problem. Do you use any of those? Try disabling them. If so, you should definitely report this to the creator of that mod.

I don't believe I do. The thing is I can jump over the gate and reach Amber Creek, but the guy I rescued would still not be able to open the door. Do you know how I could contact the creator? Thank you for your help btw

I am the creator. :) Which gate does he stand at? To clarify, Olvir, the guard, is standing at the exterior gate without opening it? Have you run up to him and all that? He should open it as you approach.