Everything can be learned, as long as you're willing to apply yourself and commit to it.
Those are two very different skillsets though (logic and creativity, from your original question's title). You could be a very logical yet totally non-creative person.
Improve your Creativity
The best way to work on your creativity is to try new things, and to get out of your confort zone.
As an aside: creativity is a way more complex concept than one may think, and attempts at measuring it and developing it have been around for quite some time.
Improve your Logic Skills
Take Courses in Formal Logic Theory
I was already a pretty decent programmer when I was invited to follow another master's coursework which included a course on formal logic. Being not really a "formal CS theory guy", that made me discover and completely new side of the field.
What about following the next sessions of these online courses? (amongst many, many others, some taught by famed professors... or their TAs)
Books, TextBooks and Research
- Introduction to Formal Logic - Peter Smith
- Agorithms - Robert Sedgewick
Programming Exercises and Code Katas
Practice, Practice, Practice
"Good judgment comes from experience, and a lot of that comes from bad judgment."
- Rita Mae Brown, Jim Horning, Will Rogers (not sure who's the original, I've seen attributions to all 3 of them)