I did my injections in my thigh as per normal on my wedding day. I bruise quite easily, so for me, i would avoid my arms.
Don't know what your Dr is talking about "hitting muscle"? Are you especially slim? even so, you should be able to inject in your thigh, with the shorter needles.
Even on my wedding day, I went to the loo, so did my injection their...in the "powder room" bit, as it did involve quite a lot of dress manoevering.
Try your thighs...you may never go back to your stomach!