Training with a Hip labral tear

Hi, i’m a 25 years old. I was a crossfitter and a boxer for 4 years. 6 months ago i felt a sharp pain in my left hip. Couple weeks later i was diagnoised with a cam and pincer femoroacetabular impingement with anterior hip labral tear.
i was given the option of going into surgery- shaving the pincer and fixing the tear.
i Am still trying to avoid surgry. I didnt get back to crossfit. I did start going to regular gym as a rehabilitation.
i mainly do back squats, deadlifts, hip thrusts hip abductor machine.
lately i have been feeling pain in my hip which i have not felt in weeks, and i started to experience a neuropathic pain in the same leg.
Should i avoid any exercises? Do you have suggestions for me to make my training more helpful? How could i get rid of the neuropathic pain and what could cause it suddenly? Do i have to do surgery if i want to be able to run and lift heavy?