No, polar molecules need not be charged. To be polar, the molecule must have two characteristics.
a. At least one of the bonds in the molecule must be polar; i.e., there must be a difference in electronegativity of the two atoms on each end of the bond, AND
(both are necessary).
b. The molecule must NOT be symmetrical in three dimensional space.
For example, the molecule CO2. There is a difference in electronegativity (EN) between C and O; therefore, the CO bond is polar. However, the CO2 molecule in linear, that makes it symmetrical, so the polarity caused by the CO on the right is canceled by the CO on the left and the molecule as a whole is not polar.
CH4. Each CH bond is polar because there is a difference in EN BUT CH4 has a tetrahedral shape, that makes it symmetrical, and CH4 has no net dipole moment as a molecule. NH4^+ is the same.
NH3 is a different story. The NH bonds are polar because there is a difference in EN and the electronic structure of NH3 is tetrahedral. That means that there is that lone pair of electrons at one of the corners of the tetrahedron while H atoms occupy the other three corners; therefore, NH3 does have a net dipole moment and we say the NH3 molecule is polar. HCl is polar although it is linear. Etc.