Is it normal to still have sore nipples 1mth PP and ok to wear silver cups 24/7?

I’m reaching my post partum 1 month mark and I’m exclusively pumping. However I still feel that my nipples are very sore to be touched by my bra and is wearing my silver cups 24/7. Is it normal to wear silver cups for such a long duration? And normal for nips to still be sore after 1 month mark?