T BG,
You overstocked your tank without letting the water settle. You have no idea what your chemistry is like and you have no idea about the PH (yes I know that is part of the chemistry), In short, adding aeration will oxygenate. If you are going to use low cost bottom diffused aeration, it will just cause you problems. If you use a good surface aerator, you could help your issues.
A good bottom aeration system could be minimally beneficial as your water is not that deep and should not stratify much, but again surface aeration is what you are going to need if added. Good aeration is one place where you have to pay for quality.
All that said, it appears your tank is located in a protected location. Aeration would help, but you are going to have to learn about the differences and choose what will work best for you.
Adding aeration now is going to also add to your requirements to pull more fish as they get larger, or you will have a fish kill. Either way, you have caused yourself a lot of work to get back to balance point.
I know this sounds harsh, but believe me it is not meant that way. I wish you would have listened and taken a little more time to learn before buying too many fish. Your issue is correctable, but it's going to be a bit more work than I think you wanted. As you learn, your tank will be a really fun place for your children/grandchildren but it will take some time and effort.
