I carry my humalog pen in my shirt pocket 24/7, except if I am going to be outside in hot sun a lot. As long as I am comfortable my Humalog should be as well. I use a little belt pouch for my Lantus and it also hold a 3/10cc syringe or two as well as spare camera battery.
When I asked to switch from vial/syringe to a pen for my humalog my doc gave me a kit with a humalog pen, a few pin needles and it even included a case with a belt loop suitable for purse or belt.
I DO NOT take my mealtime insulin before I eat, let a lonw before I get to a restraunt. One time I went to Denny’s and service was so slow I left and went next door to Bob evans. I take my mealtime insulin after I am done. That way I can take one shot with the correct dose, I am on MDI and do a sliding scale based on carbs. this allows me more freedom to eat more, or less, than I might think or planed earlier.