does it work too if i barre the fret that is being cappoed?

so if capo = 2, i should barre second fret?
if i play C, do i play a C major chord by moving two back while my index finger barre the 1st and 3rd string at second fret?

cause this is hard....the barring finger i can only make the 3rd string sound but not the 1st string

i need some help on barring too
sometimes when i want to barre, mostly it's eith 3rd string doesn't sound or the first two strings don't sound
how can i improve on barring?

thanks in advance