Digital illustration is a very broad field and might include vector illustration, isometrics, 3-D illustration, animation (2D or 3D), video and more. While I have a BA in studio arts it was so long ago no digital was involved at all! I did pursue an additional AA in graphic design more recently to boost my job search but what I have found is that it's really your portfolio that drives if you are seen as "professional" or not. While some of the GD classes were helpful, the majority of the skills I learned on my own. They are a vast amount of online courses and many of them are free classes if you don't need the credits or tutorials. Class Central is a great hub to find classes: https://www.classcentral.com/. Another trick is to research a school program you think fits your illustration niche, take their list of required classes to build a checklist of skills you need to acquire. There are also many groups you can find online with other artists to help get critiques and exchange information when stuck.
School is definitely a good option, but many can be expensive and you don't want to start out in debt. Community Colleges often have good programs for low cost, many have online classes so you are not limited by location. The benefit of that is getting feedback from teacher and students, and also access to free resources like trials or deep discounts for Adobe programs or similar.
Hope that helps a bit.