The safest option for case of bleeding gastric ulcer is paracetamol. But the pain caused by a bulging disc is less likely to be controlled by this. The other options are
Natural opiates . These are Codeine and hydrocodeine. These are not causing relief to your pain.
Semi-synthetic opioids. These are created from the natural opiates, such as hydromorphone, hydrocodone, oxycodone, oxymorphone, desomorphine, diacetylmorphine (heroin), nicomorphine, dipropanoylmorphine, benzylmorphine and ethylmorphine and buprenorphine;
Fully synthetic opioids. These are such fentanyl, pethidine, methadone, tramadol and dextropropoxyphene;
Tramadol and tapentadol are good options for pain relief.
Most of the above drugs are available on prescription. I would recommend you to discuss these options with your doctor.
Hope this information is helpful