Yes an ulcer can cause left side pain so if you're having pain on the left side that keeps coming back or doesn't go away then you should see a doctor to get tested for the ulcers.
When you have ulcers the main and most common symptom of ulcers are abdominal pain.
Most people who suffer from ulcers complain of a gnawing or burning pain that is usually located in the pit of the stomach or just below the ribs on either the right or left side.
So if you have pain in either of those areas or pain like I described then you likely have an ulcer and should see a doctor.
Most ulcers that are not too severe tend to heal up on their own within a few weeks to a few months but more severe ulcers that are left untreated may burst which can then be life threatening and require immediate surgery.