What could cause a feeling of pressure on the eye if you do not have glaucoma or sinus problems?

Dry eyes. I find that most people who feel pressure in their eyes is from dry eyes. Most people with glaucoma can't 'feel' their pressure.
Many. Sensations in or around the eye can be referred from many places, so it's best to get an eye exam to check to make sure all the eye structures are healthy. Take note of any associated symptoms that may point to another system that could be affected.