Can a septorhinoplasty be performed under general anesthesia without epinephrine? Are there alternative opinions?

It would be helpful to clarify the nature of your sensitivity, but for the sake of this question I’ll assume you’ve had injections of local anesthetic containing epinephrine and that even this small amount injected into your skin led to unwanted effects. It’s worth considering that while you are under general anesthetic, these effects would be dampened and likely resolved by the time you wake up.
That being said, my injection solution includes TXA, which helps to control bleeding without vasoconstriction, and epinephrine. Without epinephrine, your surgery will likely take a little longer as your surgeon’s visualization will be impacted, but it’s not impossible.
I recommend having a discussion with your rhinoplasty surgeon about your concerns.

Many people have rapid heart beat from epinephrine when they go to the dentist. This is less likely to occur with rhinoplasty and the anesthesiologist will be able to control your heart rate