I would suggest to do something like the following post explained.
Basically they make use of the AutoRotate property, lock the Mouse in the Centre etc.
(Oh yeah they included a CameraOffset animation, which is quite nice.)
humanoid.CameraOffset = isShiftLockToggled and humanoid.CameraOffset:Lerp(Vector3.new(2), dt * 1.5) or humanoid.CameraOffset:Lerp(Vector3.new(), dt * 1.5)
As well as use a different way of rotating:
local x, y, z = camera.CFrame:ToOrientation();
humanoidRootPart.CFrame = humanoidRootPart.CFrame:Lerp(CFrame.new(humanoidRootPart.Position) * CFrame.Angles(0, y, 0), dt * 5)
I would say that the last part of the script could possibly fix it.