Is a bachelor in Computer Science Engineering a viable idea if my ultimate objective is to be a mathematical modelling engineer? I want to mathematically model reality and use these models to solve problems. Will a degree in Computer Science Engineering allow me to do this?

Additional background. Reading the overview of a master's graduate degree (MSC to be exact) in modelling mechanical engineer, it really spiked my interest. I am not a mathematical genius though, and I need to at least see applications and more or less concrete problems/implementations. Also relevant could be that I am a senior in high school and I learned programming all by myself.

Systems I would find interesting to get to know better by creating mathematical models

I am most interested in physics and general mathematical patterns, like the approach found in Albert-László Barabási's book Network Science. 
I am not interested in specializing in any particular field just because of the field itself.
From my own experience, Im doing PhD in computer graphics, mainly physics simulation, and I have a master in mathematics, the program was called "mathematical modeling" it was mainly analysis, partial differential equations, numerical analysis and continuum mechanics.

Physics simulation is nothing else then solving partial differential equations and I can see that a math background is much more useful then computer science background when I look at my peers.

So I would recomend a math degree with a focus on numerics and physics.



edit: I see that you are a little bit worried to study math, that it might be way too much math for your taste. However, you are in a great position because you have a great motivation to study mathematics. You can always come up with things to model with math you are being thaught at school. From using projective spaces in computer graphics to fourier analysis in image processing . BUT remember one think. Do not expect that profesors will motivate you(it is a bonus if they do) but you have to activelly look for things that motivate you, everyone gets excited by different things.