Hi and welcome to the Chiari forum.
First, a NS(Neurosurgeon ) will offer to do surgery, as that is what they do, but unless they are a true Chiari specialist...do not allow them to touch you. Having a DX of Chiari is not a reason to think you need surgery....there are several tests you need to have done, but you also need to research Drs to find one that is well informed and experienced before getting upset and stressing yourself out. Stress can actually cause symptoms to flare...so do what you can to relax.
Know that your NS should set several tests up and consider those results before having any conversation on if your Chiari is mild (small herniation) or severe (large herniation)- Chiari is not the herniation, but the Malformation of the skull..so other areas need to be considered as they play a role in what is the best way to proceed.
Many Drs look to the size of herniation to determine if the patient is in need of surgery....to help you understand what I am trying to say....imagine a funnel and it's your posterior fossa, now drop a piece of shoestring licorice down it.....even with the licorice, fluid can still pass with no problems. But now place a gumdrop in there with the smaller part in first....it will cork up the opening....SO you can see how the size really doesn't make this worse....Drs that only look for the herniation to be 5mm's or more are not well experienced with Chiari. I have heard so many say "My Dr said my Chiari needs surgery right away due to the 12mm herniation...!! They never did a CINE MRI or other testing to rule out other related conditions ...IF there is no obstruction to CSF flow, surgery may not cause any benefits....it may actually cause more symptoms or issues due to having surgery.
Surgery is done to restore CSF flow and slow progression of the condition....when there is an obstruction to flow, a syrinx can form, and a syrinx depending where it forms can cause pressure to be on the spinal cord or even the brain stem....so if there is no obstruction, surgery should not be an option....UNLESS the Dr sees other issues because they looked further into your issues with testing....a retroflexed odontoid, Cervicocranial instability, are a few things in addition to a syrinx that could warrant surgery.
Be aware of all the related conditions so you know what questions to ask, or take note of what the Dr does not talk about....you will then know if this is the right Dr for you.