Now that we know this, we are struggling to find an idea that we can build, but also have time to grow during the school year as well.
Create/brainstorm solutions to all of these problems you encounter. And work through a realistic way to implement the solutions.
Some of these ideas/solutions will be terrible. Most won't make sense as a business, or won't have a market, or will be beyond what you think you're capable of. But something should stick. MVP it, and then iterate.
Since you are interning go and talk to the sales, marketing and business dev teams and ask them questions. As an intern you have the freedom to ask all kinds of questions and no one will really think twice. Just try to get away from the development group when you are asking a lot of the questions because they typically aren't seeing the opportunities only the items presented to them, and many times their presence will keep sales teams from speaking freely.
Your smart to not just jump on an idea, if you don't like it or don't feel totally energized by it then it isn't a good fit for you. Doesn't mean someone can't do it and be successful, but you likely wouldn't if you aren't totally engaged and super energized.
Keep it up and Good luck!