Apply cold compress over the breasts for 5-10 minutes right before pumping or latching to reduce swelling. When the breasts are less swollen, milk can flow more easily. Do not massage forcefully.
Do not get discouraged by low supply. That is normal at this stage, when body is still producing colostrum instead of mature milk (when the milk turns completely white). Continue latching on demand, or pumping 3 hourly. For some moms, hand expression may be a more efficient way of milk removal at this stage, until the colostrum has turned into mature milk.
If pain is disturbing, take anti-inflammatory medication such as neurofen or ibuprofen. They are breastfeeding-friendly - just make sure that you are not allergic to them!