How is it possible to distinguish antimony from lead?
As mentioned in the comments, you could perform Archimedes' Experiment.


Firstly, take the mass ($m$) (in grams) of your sample.
Then, measure the volume $V$ displaced (according to the first link), in a method summarised in the image below:




You could use any kitchen graduated container. Even though these have graduations for mL (millilitres) and even though the water density changes with temperature (source:USGS), for the temperatures in a home experiment, the following conversion could be used 1 mL = 1 cm3 of water displaced.


Then determine the density by $\rho = \frac{m}{V}$ and compare it to the known values for lead at 11.3 g.cm-3 and antimony at 6.7 g.cm-3.  


Another observed feature is that according to the LennTech site for lead is that as opposed to antimony, lead will tarnish on exposure to air.