You've not posted a link to your photodiode, or other wise defined the signal you expect from the diode so no one can check your calculations for gain. I'm going to ignore all that, because I think your dificulties are more basic. I'm going to make a couple of suggestions that you can try out easily.

1. Biggest thing is, don't use a USB battery bank. The output of those things is noisy. Use three AA cells in series to get 4.5V, and test your circuit again. If the noise improves drastically, then you can work on getting a clean 5V source. Probably better to use a low noise linear regulator. You'll have to have a higher input voltage (maybe 7V) at the input to the regulator.
2. Shorten the wires in your circuit. You have an amplifier with a lot of gain. Each wire acts as an antenna. The wires can pick up noise and interference from the environment, and your amplifier will happily amplify the noise along with your signal.

Removing the bias circuit (the two resistors and the capacitor you scratched out) was probably a bad idea. TI didn't put it there for giggles. If it made your noise situation worse, I think there's a fair chance it was because your power source is too noisy.

You may want to check your 5V supply before changing things. Hook it up to an oscilloscope and have a look.

You've not posted a link to your photodiode, or other wise defined the signal you expect from the diode so no one can check your calculations for gain. I'm going to ignore all that, because I think your difficulties are more basic. I'm going to make a couple of suggestions that you can try out easily.

1. Biggest thing is, don't use a USB battery bank. The output of those things is noisy. Use three AA cells in series to get 4.5V, and test your circuit again. If the noise improves drastically, then you can work on getting a clean 5V source. Probably better to use a low noise linear regulator. You'll have to have a higher input voltage (maybe 7V) at the input to the regulator.
2. Shorten the wires in your circuit. You have an amplifier with a lot of gain. Each wire acts as an antenna. The wires can pick up noise and interference from the environment, and your amplifier will happily amplify the noise along with your signal.

Removing the bias circuit (the two resistors and the capacitor you scratched out) was probably a bad idea. TI didn't put it there for giggles. If it made your noise situation worse, I think there's a fair chance it was because your power source is too noisy.

You may want to check your 5V supply before changing things. Hook it up to an oscilloscope and have a look.