There are three concepts I want to talk about, all involving the word “narrow”.
LEDs and photo transistors come in many types. Use the type with a narrow angle. Some send/receive light over 180 degrees. Do not use these. I am using LEDs with 10 degrees. There is much more power sent to the receiver. You must aim the devices. Lenses and reflectors help reduce the light angle. I have LEDs that put most all their power into a 20cm circle at a distance of 17meters. (using a reflector)
If you are transmitting in IR then the receiver should only see IR. That’s why some receivers come in a black case. If you can block out visible light then the receiver will see less background noise. Narrow down the range of light the receiver can see.
Normally I modulate the light with a 30khz signal like you tried first. I do not send data! I do not know why the TSOP2233 did not work. Fluorescent light has noise at 120hz and harmonics into the many khz. After you detect the light if you use several stages of 20khz low-pass filters you will remove light from low frequency sources. Just like a radio receiver does not look for information from all frequencies but is tuned to look only at one frequency, your light receiver will be better if you only look at light modulated at 30khz. Once again narrow down the range of light you are detecting.
TSOP2233:
Look at the data sheet. It is built to respond to light at 800 to 1100 nm wavelength. (Fig 11.) Because of the IR filter over the part many kinds of light are removed.
(Fig 5) It responds to light modulated with a tone and rejects light with out a tone. (33khz)
(Fig12) It has a 55 degree angle. If you can reduce that it will be better. Long black tube, lens, reflector etc.
Last thought. The TSOP2233 should work but maybe you are right it needs “data”. By adding a simple ripple counter like the MC4060 (4020 or 4040) to your transmitter you can make a signal much like the TSOP2233 was built to receive. I would try to send 64 cycles of the 33khz then not send the next (64*3) cycles. If you read “Suitable Data Formats” they talk about sending 10 to 70 cycles then waiting for 4 times that time before sending again. If you take a ripple counter and OR together the 32khz output, the divide by 128 and then divide by 256 output, you will get a 33khz signal that is on for 64 cycles out of 256. (if I did the math correct)