Seeing as I am not on T I can't give a lot of answers - however, from my knowledge, self-injecting doesn't hurt any more than injections given by medical professionals. It can be difficult, but only in the psychological sense; many people find it hard to convince themselves to stab themselves with a needle. There is certainly a bit of a barrier to overleap, but it is very possible.
Also, generally speaking, the size and visibility of veins is effected by your body fat percentage. Although testosterone can lower body fat percentage, a lot of it has to do with your lifestyle - eating habits and exercise habits. So if you were to eat well and exercise on testosterone, then most likely, yes, your body fat percentage would lower and your veins would be more visible. However, some people just have small veins and T might do nothing to help.