The video card fan is usually from a miserable quality and get problems just after the warranty period. Replacement is an option but than you have to find an identical fan with a higher quality. I have two alternative solutions to the problem of a noisy video card fan.

Repair with a paper clip

This solution costs nothing but does not last forever. Adjust the spring force such that the fan is running smoothly and quiet.

Repair by an external fan

Remove the fan on the video card and place a bigger fan 8x8cm as shown. The advantage is that a large fan makes less noise than a small one. A cooling fan is available from about 5$.