Many people use modules or cell packs. Some use seed trays and some use small pots. The actual container is less important than the moisture, temperature and light conditions. Your seedlings now need pricking out into individual containers as you plan. Btw there's a GW forum for Growing from Seed. Perhaps you didn't choose the right search terms but there really is a lot of info on the web. I googled 'Growing from seed indoors' and got lots of hit including pictures showing various containers. For how to move them into pots google 'pricking out'.

Aha! So maybe I didn't actually do this incorrectly then. I "pricked out" 15 bee balm seeds this morning. Can't wait to get home from work to see how they've fared.

Ilovecucumbers, my eyes are not what they used to be, so I find it easier to sow 3-4-5 seeds in small square plastic pots, which then fit into a tray. All you have to do is thin the seedlings to select the strongest one for each pot, and you are set for a few weeks. The trays are easy to move around, take in and out of the house for hardening off, planting etc. It requires an initial investment, but if you start plants from seed every year, it's well worth it. I got mine from Johnny's Selected Seeds a decade ago, and they still work. This is an image of a similar setup. I don't recommend cardboard disposable pots as they dry out fast in the dry home environment.

I will be doing this next year for sure. Thank you! I'm happy to say that all of the plants I've pricked out are doing fine!