What bugs you here is that the word "speed" isn't precise at all when we talk about a wave in a dispersive medium, such as water. What we usually refer to when we say the "speed of light" is the constant we call $c = 299792458$ m/s, which is equal to the velocity of light in the vacuum. Vacuum is non-dispersive, so the group and phase velocity are the same, and are equal to $c$.
Also, it is not very precise to say that "photons" travel at a certain "speed" inside a medium. Photons are quantum excitations of the electric field in the vacuum.
When we talk about a transparent dielectric medium, the excitations are quantised polarization waves : depending on the precise microscopic details of your medium, the dispersion relation can be different of just $\omega = k c$ ($k$ being the wavevector), which holds in vacuum. If the medium is dispersive, group and phase velocity are different. If you take a polychromatic light travelling through water, its group velocity will be less than $c$, thus the light will appear to travel slower.
To sum it all up, you can think of it like this : as long as you consider a linear propagation (which means you light is not too intense), frequency will never change, regardless of which medium you're travelling through. If you are inside the vacuum, velocity is $c$ and the wavelenght is just $\frac{c}{\lambda}$. Once you enter the medium, you get a non-trivial dispersion relation $\omega(k)$. Then, the light appears to be moving at a velocity given by $\frac{d \omega(k)}{dk}$, which is the group velocity, it is usually lower than $c$.
To awnser your original question yes, wavelenght of "photons" depend on the medium, it is just that light in a medium is a bit more complicated than just a photon.