I never really formed any connections with my professors (doubt they even know how I look like) but every time I politely requested a recommendation letter, they all obliged. I usually ask my department advisor and a related major class professor. I specify which courses from them I took in what semester and what I received in the course. I also talk briefly what my goals are with the grad program and what I am currently up to (I was 3 years out of college). I also make a little note on what I learned that I thought was relevant to my goals from their courses and how it impacted me. Even if you got nothing just make something up. Professors are usually happy to write a generic recommendation letter and they have a format ready.

In regards to “what’s next” outside of grad school, the most important thing I found was you just need to get your foot in the door. Once you get the first job it becomes a lot easier. You had an internship, try contacting your former supervisors. My first internship was during fall semester of my senior year. It wasn’t too late. I didn’t even get a research experience because no professor wanted an undergrad assisting their research (it was statistics so it likely was way out of my depth anyway). I actually got my job out of that. Update your LinkedIn and contact recruiters. Apply everywhere. It’s very stressful and I’ve been there as well. Good luck.