I'm kind of late to the party here, and mostly read the first page of replies so sorry if my response isn't in line with the current conversation.
Anyway, I just wanted to say I'm sorry you're having these problems and I hope you won't let them stand in the way of achieving what you want to achieve!
I remember starting to have a problem like you describe (being "behind in processing" while someone is talking) when I was about 15, and having it get worse in college and especially after college when I was just starting as a nurse. My tumor was diagnosed when I was 23. After surgery I felt I had a lot of problems cognitively but that no one wanted to believe me, especially the surgeon. (You know, since the tumor wasn't in 'cognitive' areas of the brain it couldn't possibly be affected and all that. Which I think is a bunch of crap.) The person who did believe me was my physical therapist who saw me three times a week, and she referred me to a speech language pathologist, who did an executive functioning test and found I did have some deficits, especially in attention. I felt like this proved that it wasn't really all 'in my head', so to speak, as some people made me feel, but that there might be a real issue to work on. After about a month of really working on puzzles and different cognitive tasks (I used the website lumosity.com) I had the testing re-done and my scores were a lot better - but most importantly I felt much more "with it". I
I tell you all this mostly to say it is possible that the tumor has had a cognitive effect on you, but there are things you can do to help yourself! Maybe it would be worth it to try to be seen by a speech language pathologist. Maybe they can help you figure out where the 'processing delay' is coming from and suggest how to improve it?