Auto trans not engaging

[Too Short]

I was driving my car the other day and hit the kick down and when it went to shift would not engage in gear. I restarted it and it was making a whining noise (sounded like a pump) and went in to gear. It drove fine for a mile or two and then if i came to a stop it would not go out of first gear and eventually not engage in to gear anymore. Could this be my pump to my trans and or the screen? If so are these easy to get to if at all?

Thanks Jared