L4-l5: compressed, 8mm one side- other 16mm. l5-s1: bulging disc with a 5mm mass effect. shooting pain down my leg & numbness. will i need surgery?

Differs: Each person is different. The overall response to conservative therapy (Physical therapy and Epidural injections and meds) depends on several factors: your weight, your core strength, your height, your genetic spinal canal width/height, etc. If you are short and fat, you are much more likely to need surgery with the described disc. If you are taller and slimmer, you are less likely.