beginner: homemade LED matrix

So this is my first project that isn't a tutorial and I may have gotten a bit ahead of myself. I've built an LED matrix ( 15 x 8 ) with the hopes of making a 3-letter display. I've connected all of the anodes into 8 rows and all the cathodes into 15 columns. What I have right now is very similar to the example in this video (though slightly different dimensions)

I'm looking for guidance as to how I should best control such a thing. At first I was thinking I'd just be multiplexing through the 8 rows and have a transistor for each column of cathodes, but now I'm realizing that the same voltage powering anywhere from 1 to 15 LEDs will result in either dimming the lights to nothingness or destroying them (I think).

So have I completely doomed myself? I see others that have made their own grids in similar ways but they all seem to use drivers to control them.

If I'm not doomed, what basic concepts do I need to understand or seek out to make this work?

Thank you for your time.

Your matrix will have only one column on at a time. Assuming that the LED current will be 10 mA or less you only need one current limiting resistor between each row driving pin and each row of LEDs. You need the transistors for the columns because if all 8 LEDs in a column are on, the column driver might have to sink 80 mA (More than the 40 a bare Arduino pin can handle).