I love solving/playing many kinds of logic puzzles, problems, and games. I also tend strongly towards the creative. Here's what I suggest for training your brain to be more logically astute.
First learn to reduce every bit of data to a clear yes-or-no question. Locate the information you have about a subject and identify each piece of data separately as being definitely correct (true with certainty), definitely incorrect (false with certainty), or uncertain (not yet enough information). Don't allow assumptions; they're uncertain.
A 2nd step in the logic-training department is to compare bits of information to see how the truth or falsehood of one bit affects another; e.g., "Since X is true (or false), what consequence does that have for Y?" Even more complicated is the process of using several bits of information at the same time to help move other bits into or out of the realm of certainty.
In discussions and arguments, the biggest problem I see, re "logic," is that people often place their own information in the "definitely true" category and their opponent's in the "definitely false" category. Very few are willing to admit that a great deal of it should just stay in the "uncertain" category.
Add to that the fact that people who think of themselves as "logical" seem to tend to use it as a label to verify their superiority, and they bash their opponent by calling them, or their way of thinking, "illogical." It is one way of trying to gain the upper hand in an argument. But in truth, a creative thinker may actually simply be very comfortable with looking at "facts" from different angles and seeing that what has previously seemed so certain should be questioned more thoroughly. In their defense, the truly logical thinkers (not the self-styled ones) tend to have a very high threshold for proof.
In logic puzzles, enough information is given to allow an experienced solver always to be able to find a solution - not always the case with the logical predicaments we find in life or discussions. Sometimes the complete set of facts about a subject may not be revealed in our lifetime. Uncertainty is a part of life, and it is useful to find the skills to cope with it.
Last, in everyday logic, some information carries more weight than other info does and should be heeded more (deal breakers and makers). Sometimes, a likely or possible uncertainty should be more important than a certainty. That's why motorcyclists are encouraged or mandated to wear helmets