Many people get through Calculus by memorizing formulae. But you'll learn best by combining "conceptual understanding" with "procedural knowledge".
To answer your question regarding how to develop the "problem-solving" creativity needed to manipulate expressions into forms you can apply theory:
Answer: Practice! AND Effort (Perseverance)!, AND Time (Patience)!
Practice: Math is not a spectator sport! The more problems you encounter, the more strategies and techniques you'll encounter, and interacting with both problems and their solutions will build your "repertoire": some tools you'll be able to use when encountering similar problems.
Perseverance: Keep at it! What might seem like "tricks" at first, or what might seem as "creative" now, will become "second nature" to you in no time at all, if you acquire "working knowledge" of how to use the "tools" you acquire!
Patience: Already addressed, in part. Proficiency, creativity, and mastery can be developed and nurtured with effort, practice, and time. No need to feel intimidated if you don't immediately "get" it. The creativity you speak of is a reflection of the collaborative work of mathematicians over time, each learning from one another...No one "knows it all" from the "get-go."
So, in short: You'll be on your way if you commit to the "three P's":
Practice, perseverance, and patience.
EDIT - One point of observation: The mere fact that you are questioning your strategies, wondering about creativity, thinking about how to merge conceptual understanding with procedural efficacy when attacking problems: these are all indicators that you are engaging in "meta-cognitive" scrutiny. That is, you're thinking about how you think mathematically, questioning how to best learn, and scrutinizing your current "plan of attack" with the aim to develop greater procedural flexibility in applying what you're learning accurately and creatively. These are all good things. Self-awareness and self-examination are key components to effective learning, and they indicate your recognition that you are an active player in your own education.
One book I highly recommend to anyone/everyone serious about mathematics is the book authored by Mason, Burton, and Stacey' Thinking Mathematically. When you're not under the grind with homework and/or exams, or can otherwise find the time, you might want to "have a read."