Do you have your own sound booth and calibrated equipment?
I don't, but I don't think I need it. I have equipment that gives me an audiogram within 5 dB of a "professional audiogram" as performed by pro audiologists (at all tested frequencies). That equipment is my iPhone and Apple ear buds.
That's accurate enough for me. My audiologist tells me that their own audiograms are within 5-10 dB anyways.
The setup can be a bit annoying to do at home, and I'll admit I've had to do a bunch of "retakes" when an airplane decided to fly over my house during the test, but I'd generally get what I need in less than 20 minutes.
The lack of properly calibrated equipment has a much bigger impact on the establishment of your hearing threshold in absolute value than it does on figuring the loudness of your T in dB SL, since you only have to measure a difference in signal intensity, which is less volatile across hardware. The calibration is useful to determine the intensity of the electrical signal to send to reach a given dB rating at a given frequency, but that isn't what we are doing here.
Still, as per my previous paragraph, some "off the shelf" equipment can give you surprisingly good results.
In term of pinpointing T frequency, it's very rare (I've never seen it) to send an electrical sine wave at frequency f and get a sound wave at frequency that different from f, given the way speakers work (assuming no clipping from an amp stage, etc). It's possible that the frequency response of the hardware is different (in terms of gain), so you'd get a sound that has a different volume across hardware, but unlikely a significantly different frequency, especially in the traditionally audible bands.