I’ve had to get over a blood phobia as I needed lots of regular blood tests. I totally understand how you feel and have developed a bunch of coping strategies!
My top tips are:
Go with someone who can take you home after if needs be and so you don’t have to drive with your arm after if the thought of bending it freaks you out (or perhaps that’s just me)
wear a thin shirt sleeved top for easy access.
Take a bottle of water for after in case you need a drink if your tummy’s a bit unsettled with nerves.
I’d ask to lie down for it and tell the nurse “I can’t hold a bit of cotton wool over the injection site after or take anything to do with this sorry as it freaks me out and I’ll faint so it’s over to you while I try and think about something else and pretend I’m not here, I’m so sorry!”
I’d also take a facecloth and prior I’d ask if I could run it under the cold tap so i could put it on my forehead. It really helped A LOT. The colder the better (take it in a resealable sandwich bag as it will be soaking wet on your way home)
Take a plaster. A very sticky good quality one, not cheap crap! Have it in your jeans pocket ready to whip out and give to her to put on. Just in case they don’t have any as you don’t want to see the puncture later on! Gross. Leave it on for 24 hours so you don’t see anything. It will fall off on the shower.
Id always lie for a while after and sit up for a couple of minutes before standing so I was confident I was ok.
I’ve gotten much better and now I can manage without the facecloth or drink and can hold the cotton wool. I can even take the plaster off the same day and don’t freak out about any of it at all. I haven’t sat up yet to do it but that can come in due course.
Treat yourself to something nice when you get home like biscuits or favourite tea or whatever so you associate a good memory with your visit. I know it sounds daft but the mind is a strange animal!
Facing your fears is hard but it’s a great sense of achievement when you succeed!