I was terrified of throwing up during labour. I got to 10cm but ended up in a c section because he was face up and wouldn't come out. When I got on the table, I had a panic attack and was screaming that I was going to throw up. They immediately gave me something through my IV that stopped all feelings of throwing up. Now I continued to panic a bit and I ended up getting put under general ( not trying to scare you), but the point is when it was over...I was really proud of myself and you will be too. Everyone handles childbirth and fear differently, and it's ok. You will find the strength inside you to get through.

I definitely have a phobia of barfing and that alone gave me panic attacks whenever I would look ahead to labour. Fortunately, for me, I never actually got nauseous during labour. Yeah, it hurt A LOT, but I never even felt like throwing up.

However, I did get a MASSIVE panic attack towards the end as I got the urge to push at 8cm and was not prepared for what was meant by "urge to push". It's more like an involuntary squeezing down of your entire body and I was supposed to fight that while I had 3 nurses trying to stick things up me so they could get a blood sample from my baby's scalp. The epidural had worn off so I felt everything the nurses were doing and the pain of the contractions. I ended up needing air to calm me down along with banning the word "baby" from everybody's vocabulary as it made the urge to push even worse.

In the end I needed an EMCS and was put under due to the epidural not working. I definitely would like another CS because that "urge to push" fiasco. Just the memory of it gives me another panic attack and scares me from getting pregnant again (ignoring my fears of another miscarriage or complicated pregnancy).

NICE guidelines in the UK state that they have to take you seriously and should give you the opportunity to talk to a healthcare professional who has dealt with people with similar anxieties.
If, after these discussions, you are still sure then you should be allowed to elect to have a c-section.
I'm in a similar(ish) position and I haven't broached the subject yet but I will be taking a copy of the guidelines with me once I get the appointments through.