Can we do RCT and extraction while pain?

I have ear pain, jaw pain with swelling for more than 4 weeks.I went to doctor and ENT,got antibiotics for sinus and ear infection.Even after 2 weeks,I had the same jaw pain and swelling. So I went to the dentist.He checked x-rays and said I have to remove upper wisdom tooth. He said he couldn't see any infection on any of my tooth since I taken antibiotics already. So he couldn't find the issue. He said I might have crack in lower first molar. X-ray doesn't show up anything. CBCT scan also doesn't show up.He is guessing I might have a crack or fracture and that's the reason for this jaw pain and swelling. I have sharp shooting pain in lower molar sometimes. Mostly it pain inside the ear and under the ear in the lower end jaw.Is it because of crack?Dentist told me to extraction and implant since RCT will not be successful for crack.What should be my next step?Can I try RCT if it's crack?Will Endo do immediate RCT even with pain and swelling?or after it subsides?pls help. I am in USA.