It does not work because:
- You switched the P-channel and N-channels (the P channel should be at the top, N channel at the bottom)
- The FET sources should be pointing towards the supplies (either ground or the 120V). Here, you have the top FET whose source is pointing towards the load.
- The control voltage does not have the same level as the totem pole supply voltage.
The two first problems are easy to solve. The last one, however, is a bit more difficult to fix. You need some kind of level translation to provide the appropriate gate signal to the top P-channel FET (which needs to go from 120V to ~115V), from the 0-5V signal you have as input.
What I can suggest, if the input signal is a square wave continuously oscillating, is to use a simple capacitor to shift the 0-5V signal to 115-120V. It is the simplest way (but won't work with continuous input signals).
The requirements for this to work is to choose small mosfets with very low gate charge, because they will switch fast enough. Otherwise, the rise/fall time will be too slow and both FETs will end up conducting at the same time, which is bad. The part suggestions I made on the above LTspice simulation show it can work up to the MHz range.
Probably higher with some adjustments and compromises on the power consumption.
Note that there are other possible topologies (e.g. N-channel both at the top and bottom), but they will be a bit more complicated to implement.