Will wearing sunglasses make your eyes more sensitive to the sun?

No. No, but they will reduce your risk of early cataracts, macular degeneration and eyelid skin cancers.
Possibly. If you wear sunglasses all the time your eye may temporarily find it hard to tolerate bright lights.
No. There are many reasons for sun sensitivity and most are not serious, but some are. Sunglasses can help for some of these causes, but do not cause the sensitivity to get worse. See an md (ophthalmologist) for the exact cause and appropriate treatment of any new or severe sun sensitivity.
No. Sunglasses do not change any physical attributes of your eyes. But when you remove them, you may feel like the sun is brighter because your eyes have adapted!