I can relate very well to hoe you feel and when first diagnosed I could very easily have written the feeling you express. I was diagnosed T1DM in 1957 and still don’t like giving myself shots even though I done it tens of thousands of times.
From my experience I would say that you are being a little bit too cautious; yes, there are spots I would avoid but not many. Occasionally I’d get a drop or two of blood but nothing serious; the most bleeding I’ve had has been in recent years, after I went on a blood thinner following insertion od a couple of stents, when I pull out an infusion cannula that has been in me for a few days or when I disturb a cannula during activity.
Keep up your good effort, you ARE doing the right things. I’d guess that your “little blue lines” are more visible on you than on many other people because of your skin tone - but thousands of us have used insulin for years without causing serious injury and these new needles are s comparatively tiny.