Perfect age for a new kind of seperation anxiety...the if Mommy is not in sight, she must have disappeared and who will take care of me anxiety.
My son went through the same thing, so I followed my Pediatricians advice and began involving him in my OWN routine. Had him sit and help me sort laundry (not the best job but, he loved it and still does), moved his high chair so he could watch me wash dishes/cook dinner and even started letting him help me with grocery shopping. It helped tremedously, and at this age I began to explain things to him indepth. Mommy is doing this because this has to happend, and Mommy will be going to the gym and Grandma and you get to spend time playing. Now, he has his own kids cooking set from IKEA that he uses whole I am cooking and he is such a big helper.
I don't think you're being selfish at all...a few moments at the gym, getting a haircut or just taking a shower alone are so necessary sometimes!!!
But, I think remaining consistent with the timeframe and who watches our kiddos is super important. A stranger is great, but if Grandma or someone more familiar is available, then that might help ease her out of her anxiety. Don't worry it passes! And, soon she'll be rushing you out the door...my son is now two years old and some days he's all about Mom and other days he's all about Dad...and then, there's the days when Grandma is around and I am obselete!!
Best of luck!