How much current do you want?
Your signal generator probably has an output impedance of 50R which won't give you much current so it's no wonder, when you connected the transformer, you only had 0.5mA before the voltage dropped to low.
An amplifier will saturate a bit below its supply voltage so for a peak output voltage of 110V you need a bridged amplifier with a power supply voltage of 115V, possibly even higher. For an RMS output voltage of 110V, you need a bridged amplifier with a supply voltage of at least 160VDC.
If using such a high DC voltagge power supply is not an option, then use a lower voltage audio amplfier and a transformer. As audioguru correctly stated, this is not an option for high power levels because the amplifier will loose half the power.