are there things called infrared photons, or ultraviolet photons etc, as there are infrared waves, or ultraviolet waves?
Yes, absolutely. Certain aspects of the photon notion can be thought of as even more like a classical wave than even the above. One photon alone can be in a pure quantum superposition of energy eigenstates, or polarization eigenstates. This means that it itself can have a spread of wavelengths. In principle, one can have lone, white photons (although in practice I don't know of any physical processes that can produce pure superpositons of radically different frequencies)! However, there is still a definite - albeit needfully time varying - phase relationship between the frequency components of a "white photon" quantum superposition - it is a pure and not mixed state like "everyday" white light.
How this works is the following. A "lone photon" is simply a state of the quantum electromagnetic field, see the "Quantization of the Electromagnetic Field" Wikipedia article where the number observable is certain to return a measurement of $n=1$.
Moreover, you can define probability amplitude functions of space and time from the quantized electromagnetic field that fulfill Maxwell's equations, which can thus be thought of as the analogue of the Dirac equation for the lone photon. Every classical solution of Maxwell's equations defines a corresponding one photon state and contrariwise. See my answer here for details
