First of all congratulations on the birth of your child! :)
No breastfeeding does not increase the chances of BC.
If the lump is painful,then could be a clogged milk duct which is very common in breastfeeding mothers.Your should massage the lump while breastfeeding or when pumping.Applying very warm compresses should help unclog the duct.
However,any new lump that persists,whether painful or not, needs to be evaluated.Since you are breastfeeding,it's highly unlikely to be something alarming ,but the only way to get a proper evaluation is to have this lump investigated by your OBGYN.
Hoping that this problem is nothing to worry about.
Blessings to you and your newborn!
Thanks a lot... Definetely a bit relieved