Had a student ask about becoming a professional 3D modeler here is a snippet of the question and my answer:
(Student) "I was listening to your 8a lecture where you were discussing passion versus opportunity and it got me thinking about where I stand with that. I still plan on pursuing website design for practicality, but I was wondering if you knew of any 3D modelling-related internships I could look into in case my interests in this field could develop into something professional. I really enjoy learning more about Maya with each new thing I model and would love to see the workflow in a real job environment. Also, are there any other software that I could learn to develop this skill? I know you mentioned Substance Painter for normal maps, would it be good to learn any other specific programs?"
These are really deep considerations, and I appreciate that you are thinking and thinking this way: practical and fanciful. I think really, the thing to do is to keep practicing modeling, especially in the case that you enjoy doing it. Whether or not you end up working in a field where you are modeling professionally doesn't really matter if you are enjoying yourself; however, the fact that you really enjoy doing it, means you might have that weird "modeling gene" that I have, and perhaps it could turn into a profession for you. Again, keep practicing! Learn outside of class, more advanced techniques, as this is a beginner's class, and there is much, much more to learn.
So there are many other kinds of modeling you could learn in the entertainment/graphics realm:
Procedural Modeling- Usually done in Houdini, can involve some program and scripting and math (if you want to get really good/pro at it, you gotta learn to code and do a little math). I am learning Houdini now and I love it, even as a traditional artist, once I got over the fear of coding and learning some math, I realized the potential. There are tons of free tutorials available on SideFX website, and the apprentice version of Houdini is completely free to use, though is limited in some respects (but the limitations shouldn't matter too much, you can still do most everything). As someone learning scripting and coding for web, Houdini modeling might be a perfect fit for you. Check out this tutorial demo, it is more advanced than beginner stuff, so I would not start with it, but you can see the potential. Also good Houdini Artists are usually in high demand: Lake House Tutorial Ad, SideFX software
Zbrush - for digital sculpting, there is no substitute for Zbrush, but there are a few runner-up's: Mudbox, Blender (has regular modeling (like Maya) and sculpting and is 100% free), 3D Coat, and for Ipad and Android, I suggest Nomad Sculpting. Zbrush also has a free version that is not as robust of a toolset called ZbrushCore Mini, I have never used it, so I don't know how good it is or how well it stands up to its predecessor.
And if you want to model for 3D print, you can look into Fusion 360 (I think it is free to use) as it can parametric model with exact precision. Here is an article for this type of modeling: https://www.sculpteo.com/blog/2018/03/07/top-8-of-the-best-parametric-modeling-software/
Right now I am learning Blender and Houdini. I am versed in 3Ds Max, Maya, Modo, and Zbrush, but I want to learn Blender because I see the industry starting to adopt it, and it is free so it means if you learn it you can do freelance work with it at no cost to you. To me Houdini/Blender/Zbrush is the toolset I will probably rest on for the foreseeable future, although things change so fast, who knows what is coming down the pipe? If Blender became as good of a sculptor as Zbrush, I'd just make my Pipeline Houdini/Blender.
As far as material/texture authoring, Substance is where it is at right now. There is a really amazing 3D painting program called Mari, but it is usually only used in big Hollywood studios. Zbrush also allows you to paint on your model, but I would still lean more towards Substance, it is a much better method than what Zbrush uses. 3D Coat also has good painting from what I have heard.
So, let me not forget that you asked about internships in modeling. I did an internship like that at Midway Games years ago. I am not sure what is out there right now, but the key to getting an internship like that is to get really, really good at modeling and make a portfolio with no less than 3 top notch models to show your work. Then find out if there is any internships and get into the running for the internship. Word of advice: Learn to model photorealistic, most places, even a place like Pixar wants to know you can do photorealism.
Here is a look at a great Modeling Demo Reel that might give you some direction. I am using this reel because I checked and she was working in the industry when I first saw this; it means she was hirable: Emily Bélanger - Modeling & Texturing Demo Reel
Hope that helps give you some direction!
Daniel Triplett, is an artist that worked in game development for over 6 years, and now teaches in the Computer Graphics Technology department (CGT) at Purdue University.