Earlier quoted context omitted.
I went back to school with the same fears. It comes back to you.
Genuinely, thanks for sharing. I always want to go back, but fear I'll embarrass myself. Or at least realize my age is catching up eith me. Out of curiosity, what did you go back for, and how did it go?
Do you practice doing long division every day, without pen and paper? If not, then I think you ought to try that before making the judgement "I can't do it". Practice is very important, especially when it comes to memory intensive tasks. The other key bit is coming up with efficient algorithms for doing division in your head that take into account the pros/cons of memory vs. pen and paper (why should we expect algorithms that run well on paper to be effective in our memory-only execution as well?). Over the years, people have developed a wide variety of "mental arithmetic" algorithms.
Finally, doing long division in your head isn't important. No one will judge you by it, when you're applying for a PhD, and so you should not judge yourself by it. There are way bigger fish to fry, even in mathematics.