“Should I keep eating if constipated?”

Yes, of course you need to eat and drink fluids to maintain nutrition and hydration. Constipation is caused by a slow colon, usually. Best to increase fiber in the diet (e.g., citrucel 1 TBSP three times per day), eat a lot of fruits (prunes, kiwis, grapes etc), and start laxatives such as dulcolax and Miralax. Smooth move tea can work as well. See a PCP or GI doctor if over-the-counter laxatives are not helping.