Based on supplemental research I've done on this issue, the primary reason nurses seem to be trained to administer injections quickly is to avoid anxiety and perceived pain at the time of injection with the large number of patients made uncomfortable by needles: particularly children. You should insert the needle quickly, gently attempt to "register" the shot (pull back on the plunger) to make sure you've not hit a blood vessel, (in which case you'll see blood in the barrel,) and proceed to inject the fluid at whatever speed you're most comfortable. If you're uncomfortable with having a needle stuck in you for thirty seconds, and the feeling of the injected fluid causing pressure in you muscle causes anxiety and makes you feel faint, feel free to go quickly, but know that the speed of injection makes no difference in the efficacy of the administered medication. If, however, you wish to avoid lasting discomfort and are not uncomfortable with injections in general, go slowly. You may also want to avoid exercising, sitting on, or massaging the injection site for ten to fifteen minutes after administration, while the fluid is still being evenly distributed.
Prior to the first time I injected anything, needles made me very uncomfortable and faint. I quickly grew comfortable with it by associating the injection with the effect of whatever it was I was putting in myself, and am no longer bothered in the slightest by them, in spite of the fact that I haven't used one in years. If needles make you uncomfortable, try thinking about what the estrogen is going to do for you as you do it. Having a positive association will help things become easier, in much the same way it did for me when I came to associate needles with a huge surge of dopamine. It does get easier. I promise.