This short message by Timothy Keller (picture below) assures me that:
1) The short answer is Yes. There is no limit to the Grace coming from above.
2) The more important point of repentance is true repentance. Not partial repentance.
3) You shouldn't be worried about whether God is going to throw you away. you should be worrying about what was the root of your sin. Identify it so you can get over it.
Here's the link so whoever wants to see it can go see it. May it bring you comfort and challenge you today. For living right is harder than saying sorry.
"If you didn't earn your salvation to start with, how are you going to un-earn it?" - Tim Keller.