How to calculate p-values for fold changes?
Your null hypothesis would be that the fold-changes are 0, so you can either do the T-test accordingly or simply do away with the fold changes and perform the T-test between the raw values in the group (this is preferable to performing a T-test of one group vs. 0, since it allows you to assess the expected variability around 0). Note, however, that 3 samples is pretty much the bare minimum needed for any statistics, so your power will be terrible and your estimation of variance will likely be pretty inaccurate. Consequently, take any p-values with an appropriate grain of salt.

To my knowledge there aren't any good alternatives for your situation without having a good expected background distribution.