I'm only 2 months into insulin or there abouts myself.
I still have a few occasions where I think 'ouch' in advance eventhough I know it doesn't really hurt. My first injection took me an hour to do, lol - sweating and panting. Sorry about the lol, but I'm normally not like that. I think my tactic after a bit was to think that the sooner I got it done, the less upset I would manage to get about it - because I wasn't upset about 'it'. I was upset about the unknown really - insulin is 'dangerous', I thought, what if I do it wrong, what if I take too much or inject it wrong. Lots of things I didn't know. I was almost ready to have a tattoo on my tummy putting lines where the nurse had said I could inject so I didn't make a 1mm error.
It all got far easier with a bit of time, but I find if I am in a hurry to do my injection it can still pop up a bit sometimes - the fear that I may forget something, I guess.
This is a rare occasion though - most times it's just needle, dial, jab, press, wait, done.
I think if you get to a point where you just 'can't', put the kit down for a couple minutes - breathe, turn on the radio, be ready and then go do it in 1 go and 'think about it afterwards'. Once you have a handful good experiences in, then I think you'll be less likely to be upset. You can put too much pressure on yourself in 1 session, so you start automatically panicking. Break it up and come back to it 2 minutes later - can make a world of difference - at least it did for me in the beginning.