If you're using the silicone flanges to control elasticity, you can't use any oil-based moisturization because it would keep the tacky silicone from holding your nipples so they don't stretch too far. But nipples with normal healthy tissue shouldn't need extra moisture.
Try spreading your own milk on your nipples after pumping. It's anti-inflammatory and has water-based lipids (fats) that can be soothing. If that doesn't help enough, it's important to rule out infection. Feel free to reach out to our inhouse lactation consultant for guidance.