How can I tell whether my eye injury is severe enough to see a doctor?

Eye injury. Generally any eye injury should be evaluated by an md because your personal evaluation cannot necessarily detect problems that may require treatment. Particularly important to have a prompt evaluation for change in vision, pain, floaters, flashes, bruising, scratchy sensation, double vision, discharges, loss of vision, just to name a few.
Vision changes. Anything that causes visual changes, pain, floaters or double vision should be evaluated quickly. If uncertain, get examined - reassurance is priceless!