How to increase laser/light frequency?
I think you are confusing the energy of the laser as a whole and the energy of the photons in the light.

As you say, the energy of a photon is exactly proportional to the wavelength or frequency of that photon. If you have a higher energy photon, it will have a shorter wavelength. From wikipedia:

''
The equation for photon energy is

$$E = \frac{hc}{\lambda}$$

Where \$E\$ is photon energy, \$h\$ is the Planck constant, \$c\$ is the speed of light in vacuum and \$λ\$ is the photon's wavelength. As \$h\$ and \$c\$ are both physical constants, photon energy changes with direct relation to wavelength \$λ\$.''

In most lasers - which is short for light amplification by stimulated emission of radiation (maybe even all, but I am not an expert on lasers) each photon is emitted by electrons that jump between orbitals (in lasers, this happens during a process called Stimulated Emission - the key to the concept of lasers), which means they decrease in energy. To do so, they must get rid of this excess energy, which they do by emission of a photon, which has this exact amount of energy. This means that all photons that are created by the many electrons making these jumps have the same energy and thus the same wavelength, and as a result, lasers have a very monochromatic (= a single wavelength) spectrum. 

When you increase the energy consumed by a laser (perhaps a laser diode?), these orbital jumps are still the same - the photons don't suddenly get more energy. However, you increase the amount of photons created ,and as such the amount of radiation energy being generated by the device. The wavelength does not change.

Also, you see to be confusing black-body radiation with lasing radiation. These are two different things. Black body radiation is generated by random energy jumps that emit photons of various wavelengths. Their distribution is discribed by Planck's law (the same guy from the constant earlier in this answer). As we increase the heat, the "peak" of this radiation also increases. This process is also where the term "Color temperature" comes from. This is different from laser radiation, as it contains a continuous spectrum of light, instead of discrete spectral lines found in lasing radiation. 

In short, I think you are confusing a few concepts, and perhaps you should look up some more information in the links provided here.