Understanding "dBc" in the context of IM3
When measuring the IM3 suppression, you take the difference between big tone and small tone, that's how it's specified, don't wory about 'total' carrier power. In this case it's 23dB (or -23dB).

To get from IM3 suppression to IP3 (making the usual assumptions***) you take the big tone + half the suppression, to get -105 + 23/2 => -93.5dB. Now as dB is a ratio, what absolute power is this? Well, it's -93.5(dB_whatever_that_scale_reference_is).

***What usual assumptions? Glad you asked. If a non-linearity is sending power to 2f-f frequencies, then for small amounts of distortion, the cubic term will be the strongest, it's a 3rd order IP. This means as we drop the power, the main tone will drop dB for dB, the 3rds will drop 3dB per dB. That's why the sum above gives you the power (the theoretical power) at which they become equal. 

However, that only works if we assume that the 3rd order terms are dominant. As the intermodulation power rises, higher order terms can cause significant distortion, changing the way the distortion power rises, and changing the validity of the main_tone+0.5suppression equation. With only 23dB suppression, I think it's possible we are in, or at least near, that region.

This means that instead of taking a single measurement, you should take a measurement at a range of power levels, and plot the IPs against the main tone power. If the plot is a straight line with gradient 3, then you can estimate IP3 from it. If it is not, then it is not possible to estimate an IP3 from it. You can quote suppression, but an extrapolation to IP3 will be meaningless. Note that some manufacturers do present a graph of IP3 versus power level, which is better than quoting a single IP3 level, but it is an admission that they are outside of the single IP3 figure range.