How to choose the dimensions for a prestressed I-beam?

Let's assume we have prestressed the beam enough so the concrete under the load has zero stress at the bottom and the and maximum at the top. and let's assume it is a 350kg/cm^2 concrete which is a lower range of prestress concrete strength.

$$ M= 1.2cdot M_{deadload}+1.6cdot M_{live load}$$

I assume your loads are distributed loads and you forgot to mention that.

$$ M= frac{1.2 *2.2kN*9^2}{8}+frac{1.6* 11kN*9^2}{ 8}=26.73 kNm+178.2 kNm=205 kNm$$ $ assuming phi=0.85, 205/0.85=241 kNm$

As a first test size, we pick $text{ h = L/20 = 45cm and b=25 cm.}$

The stress triangle is a 45cm height by 25 cm base and with 350kg/cm^2 on top of the beam and zero at the bottom.

$$C=T= 350 *45/2 *2/3*45*25= 5906250kgcm *9.8/100= 578.8kNm$$ So we are over designing by a factor of roughly 2.5.

We can now iterate down to find the right size, albeit with an eye on controlling the deflection.

This is a very basic first rough step to get an idea for the size of the beam, we need to know a lot more as to the type of strand or concrete before we can start the formal design.