TLC which control progress of organic chemical reaction indicate formation of new proposed products which by knowing polarity of it theoretically can predict my new compounds.
You can use Gaussian to measure the dipole moment of any organic molecule. For rough measure you may use Chem3D but be sure that you clean up your structure first. I guess you have these software available in your department.
There is really a lot of ways to do it. However it depends on what you feel inder term "polarity". There is a lot of software that for example predict water-octanole-1 distribution coefficient. The easiest way is to draw molecule in http://www.chemicalize.org and take a look on logP values. May be it will give you some insights but bear in mind that prediction can be poor if you compound have metal ions and other not purely organic parts, or it have many tautomers (then logP will depend on tautomer you draw) or charged species.
Under polarity we also can mean dipole moment, distribution of electrostatic potential and so on. In this case the best way is to calculate it by means of quantum chemistry. However it can be easy or not - depending on software you have. Free software is harder to work and commercial are much easier. And it will be harder to do it for complicated molecules with large number of atoms.