No, you don't need to open a separate Amazon account for each country where you want to sell your products. Instead, you can sign up for an Amazon Global Selling account and list your products on the Amazon marketplace in the United States, which will automatically make them available to customers worldwide.
With Amazon Global Selling, you can reach customers in over 100 countries and territories through a single account, and Amazon will handle the local shipping, customs, and duties, as well as local customer service and returns.
This approach makes it easier and more convenient for you to sell globally, as you only need to manage your listings, product information, and inventory from one central location, rather than managing separate accounts for each country. However, it's important to research and understand the local regulations and requirements in the countries where you plan to sell, and to be aware of the potential shipping and tax implications of selling through Amazon Global Selling.