It's not anxiety, and it hasn't got anything to do with mortality or existentialism. It's the feeling one gets when one becomes acutely aware that time is passing. An observant sadness yet simultaneous joy and nostalgia. I think it is one of those things we have no words for, like sitting on a grassy hill and suddenly becoming completely aware of gravity holding you onto the earth's surface, and imagining that if it were to stop suddenly one would simply float outwards from the surface of the earth into the vast nothingness of space.
I guess what I'm trying to say is that the passage of time has a certain weight and physical element that you can feel when you get this "anxiety". Like the Vonnegut's Transmalfadorians who saw humans in the dimension on time. Some sort of other world and reality. Have you read the poem "Esse" by Milosz, I think it will bring up some of what you are feeling.