I know quite a few web developers without bachelor's degrees in computer science, but they're the exception to the norm. You may be happy with an associate's degree and less debt, that's up to you. One option is to complete your associate's degree and then dive into the job market. It may be useful for you to get some job experience before continuing on to complete a bachelor's. That experience may help you figure out which parts of design and development most appeal to you. Regardless, I would definitely double-check with your college advisor about the rules for transferring your credits / associate's degree towards a 4-year program down the road. For example, how does the web design/dev track line up with the computer science major requirements at other schools?
Ok, lastly, there will always be more demand for engineers than graphic designers. I have dabbled in both and wish I had chosen one or the other. You may want to look into engineering programs that include courses on design thinking, ux design, interaction design, etc. Those are more focused on the function and experience of using an application as opposed to the aesthetics. Having a solid foundation in both programming (code) and user experience is in my opinion more valuable than mastering both graphic design and programming.
Blaise recommends the following next steps:
- Check with your advisor about options for transfer of your associate's towards a bachelor's
- Look into user experience and interaction design, so that you're aware of how broad the software design field is