Why is my left foot swollen on the outside? Should I put on or take off shoes?

More info needed. To receive an answer that will be more helpful, you need to give more information...Your health status, any problems such as gout, diabetes or blood pressure concerns. You should state how long it has been a problem and what you do to make it feel better. Also tells us what it looks like. Is it discolored, swollen or point tender. The more you tell the better the answer.
Neither. Swelling of your feet is not normal & is probably not due to your shoes. If it persisists you should have it checked by a doctor.