For example in this three blue one brown video he shows the visualization of the derivative of x^2 it's relatively easy to see how it works and intuitively I could see how I could come up with this myself. 
On the other hand Schrödingers Equation I don't know how I am supposed to picture this or come up with this my self. 
So I guess my question is in order to come up with new formulas do I need to be able to visualize everything or just accept the pervious person formula as an absolute truth and just simply play around with adding things onto it to come up with something new and innovative to solve another problem or something similar ?
Regarding visualization: Pictures are often useful to understand a specific concept in a pure form but often different concepts are combined to such an extent that the whole cannot really be imagined as a picture anymore. Just try to imagine the derivative of $5x^5+3x^4+3x^3+2x^2-x+2$ as a picture. Schrödinger's equation tells a whole story. It's hard to summarize the Odyssey in one picture and in the same way, advanced mathematics is hard to grasp in one picture. Pictures may explain part of it or help you understand a certain aspect but you shouldn't expect everything to be explainable by a simple picture.
Visualization isn't the only way to understand things better. As human beings, we are all equipped with a variety of systems to understand the world. Visualization is one of them, but game theory can be another helpful one (if I say this how will someone else disprove me?), not to mention words, the explanation mechanism we are using in this text. If you do mathematics long enough you may develop intuition that cannot even easily be described through pictures, words or games. You may find some mathematical ideas innately beautiful or be able to draw analogies between different fields or disciplines.
Your question is a good one: how to come up with the formulas, instead of just using them? Usually, they arise when you're faced with a problem that you want to solve.
Schrödinger was looking at physics phenomena for a long time before coming up with his formula. He also had already seen many systems of differential equations work out well for other problems. He had a good grasp of which units played a role, which variables and which constants. He understood well how linear operators work and how you can use them. He had a good understanding of differentials, exponentials, complex numbers and a lot of advanced maths. He may or may not have liked cats. He then combined all of these tools into a solution for the problem which he faced. So to come up with the formula, you would need to have all of that background in both maths and physics.
More generally then, how do you come up with a formula? That depends on what you're working on. But in general, here are a few questions you should ask yourself when you're trying to come up with a formula: