What causes swollen tastebuds at the back the tongue? I have them they are not painful.

They may be normal. The taste buds at the back of the tongue appear larger than the ones towards the front. If they continue to increase in size, you should see a doctor. If there is no change, i would suggest that the next time you see a dentist or physician have them look back there and see.
Let me explain. One of the most common reasons for the eruption of sores on the tongue, both on the surface and the underside is eating very hot food, that may irritate or burn the papillae causing swelling. Having very spicy or salty food is also known to trigger swelling of the taste buds. Exposure to toxins like alcohol, tobacco smoke, insecticides, etc.