Affordable Insulin Now Act of 2023 This bill limits cost-sharing for insulin under private health insurance and establishes a program to provide insulin to individuals without insurance. Specifically, the bill caps cost-sharing under private health insurance for a month's supply of selected insulin products at $35 or 25% of a plan's negotiated price (after any price concessions), whichever is less, beginning in 2024. Further, the Department of Health and Human Services (HHS) must enter into agreements with pharmacies or health care providers to provide insulin to individuals without insurance. HHS must pay such pharmacies or providers an amount equal to the difference between the out-of-pocket cost to the individual for a 30-day supply of such insulin products and $35.