I'd be reluctant to self diagnose low supply. If you start offering that side first constantly and pumping it after a feed, you may create an oversupply issue on that side, and risk damaging your supply on your 'good' side.
Alternate start sides at every feed. Make sure you allow LO to unlatch naturally. Make sure you are offering frequent feeds. Keep yourself hydrated and rest as much as possible.
Your boobs are never empty. You don't want to be engorged, as that's your body making more than required. I only get engorged now if LO sleeps through after having a few nights of waking for feeds. The softer the breast, the higher the fat content of the milk.
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