I am hesitant of any dr that just jumps right into surgery without trying all other conservative and non-ivasive methods first!! Get 2nd and 3rd opinions from different drs. What does your mri state? Do you have a copy of the report? What are your symptoms?
The recovery can be a little rough, how bad is the compression, do you have the report? What kind of symptoms are you having?
Like my friend above said, it wouldn't be a bad idea to get another opinion or 2. This is a pretty serious procedure.
I make the assumption that you are talking about cervical discs...if you truly have cord compression, which the MRI probably would show (was it with contrast??), you very well could have long-term neurological effects if it is not relieved in a short period of time.
If you trust the spine doctor, let him repair it. As a cosmetologist, you are going to need the use of your arms your whole career.