A professor had agreed for an internship and asked me to remind her again before august starts. But she has not responded to the reminder email I sent 10 days ago . Should I mail her again? Is it impolite to call her in her office? I was very eagerly looking forward to work with her so yes, I’m slightly desperate.
It is very likely that she just overlooked the mail. You definitely should send her a mail again. It's totally reasonable to keep asking until you get the response, even if she suddenly changed her mind about hiring you.
BTW, it's summer now. Many professors would go on vacation at this moment. If this is the case, I am afraid you have to wait until she gets back to work.