It's a common mistake for beginners to read a data sheet or tutorial and misinterpret "the maximum current of the pin is X mA" to mean "the chip will safely limit the current to X mA". But in fact it means you must take care not to exceed X mA or the chip will be damaged.
I am unsure what to advise you to do. You must finish the project asap with the components you have, but you need to start over with a better understanding of circuits and leds. I think perhaps you should hand over the project as-is, with all its faults, and in the write-up, describe the errors you made, why they have the effects they do, and how you would design the circuit differently if you were starting over. At least that way you can show that you have learned from your mistakes and now better understand the principles involved. The most important lesson being "don't buy any components or plug in your soldering iron until you have had someone more experienced review your design on paper".