experimentally, the intensity of the Raman scattering is proportional to v4 (frequency of the incident radiation, C ( concentration of the species responsible for the scattering, I0( the intensity of the incident beam) and K ( a constant of the instrument). There will be no the fluresence caused by incident readiation just like what you said. But there are still some reasons for the fact you have obseved. For example, 1. the purity of the sample, the tiny paritles still have possibility to produce strong fluresence background so that you cannot directly observe the Raman signal from your sample. Usually you have to filer you sample before you use them; 2. The intensity of incident radiation you used in your experiment. If laser power is so weak, it is very impossible to get good Raman signal; 3. The concentration of sample is another possible reason. Of course, if the Raman scattering signal is weak, there is also another possibility casued by the absorbtion from the sample itself.
Good luck.