I tend to press down on my eyes when I am stressed and feel strain in my eyes. Is this okay?

Probably. Hard to hurt your eyes by pressing on them for a few seconds. Just sounds like a bad habit.
Try not to. Eyestrain usually has an underlying cause. If it is stress, then stress management techniques such as biofeedback can help. If the vision feels blurred then it's probably a good idea to get the vision checked out first - this has solved many an eyestrain complaint for us!