I had a similar issue with lenses. Those appointments are hell and counter-productive. Firstly, it's a difficult thing to do under pressure. Secondly the more you attempt it the more your eyes get irritated and the more difficult it becomes. Eventually I managed to sort of just shove it in when the optometrist wasn't looking. Then they gave me some to take home and I was able to practice in a less stressful environment and finally got the hang of it. Saying that, if I stop for a while and then go back to them it can take a couple of days to get the reflexes to slow down again. If you can order a pack online without a prescription I'd say it's relatively safe to do that and practice at home provided they've already explained the hygiene basics and you know how to put them in/out, you're just having issues with the blinking.