I have a bulged disc on lower right back. Do I need to rest or do specific exercises? The prescribed anti inflammatory pills don't seem to help.

First, a bulging . Disc is a normal finding. Treatment depends on correctly diagnosing the cause of pain. If your pain is primarily in your back, an esi is unlikely to help & if sciatic in nature, it works 50% of the time. Lifestyle factors play a role like smoking, being overweight and not exercising regularly. Medication, time, activity modification play a role. Physical therapy &/or a back support can help.
Abdominal muscles EX. A bulging disc occurs when one of the discs between your vertebrae develops a weak spot and pops out beyond its normal perimeter. Interestingly, many people might have a bulging disc and not even know it, as long as the bulging area does not press upon surrounding tissues. Do what you comfortable, i will advise to strengthen your abdominal muscles and avoid what bother from movement and exercise.