Hi Jess, and welcome (and welcome Reeceeey too - sorry, missed your intro thread!) 🙂
If it's people seeing you inject that's the problem, Jess, then yes, I used to find that difficult - I wasn't exactly anxious, but didn't like the idea people might see. I'd go and sit in the car, or in the loo (if it was an individual one with a washbasin!), or hide behind my partner, and just couldn't do it if there were people about. Now, I think it's their problem if they don't like it, not mine! But it did take a while.
If you're having trouble seeing the needles go in, Reeceeey, you could ask for covered ones - I have novofine autocover needles because I'm needle-phobic and couldn't inject at all if I could see the needle go in. They have a little cover so it's more like pushing a pen against your skin than a needle - the only thing is they are a bit longer (8mm), but you don't have to push them all the way in!