Do I need a sight test if I've been for a contact lens check-up?

Yes. 

Contact lens check-ups are designed to check the condition of the front surface of the eye, which is in contact with the lens, and to check the quality of vision whilst wearing the contact lenses. A comprehensive sight test will include a check of the health of the inner and outer parts of the eye as well as a test of vision (both with and without any current prescribed lenses). 

The back of the eye can be affected by a number of eye conditions and, although these conditions are uncommon, they may be picked up much earlier through the sight test than through waiting for symptoms to occur.