What to do when someone does not respond to your email?
First, forget your embarrassment and go see your professor for help. That is his job. If he asks why you did poorly, give him the most honest answer you can and see if he can provide some suggestions to get over the block. Your difficult with PDE is pretty common as it takes a new way of looking at things after calculus. 

As for the tutor, two days is very little time to make initial contact. So, you can ask again, in email, about current topics. But once you do make contact it may go more smoothly. But grad students are pretty busy. 

But, I also urge caution with any tutor. Make sure that they don't give you so much help with things that  you don't actually learn yourself. The best thing they can do is give you some exercises and watch as you solve them, with you expressing your thoughts on what to do verbally. The best tutor will give you only minimal hints when you get stuck, and not show you how to approach every problem.