No, you cannot make money directly from sponsored posts on a personal Facebook profile or Facebook page without using third-party apps or websites such as AdSense. Facebook does not allow individuals to make money directly from sponsored posts on their personal profiles or pages, as it goes against their community standards.
Facebook has strict policies around commercial content, and it does not allow individuals to sell or promote products or services on their personal profiles or pages, unless they have been authorized as a verified representative of a brand.
If you want to monetize your Facebook presence, you can consider promoting products or services as an affiliate marketer and earn a commission on any sales made through your unique affiliate link. However, even then, you need to be transparent about your affiliate status and ensure that your posts and promotions comply with Facebook's advertising policies.
Ultimately, if you're looking to make money through your Facebook presence, it's important to familiarize yourself with Facebook's policies and guidelines and to be transparent and honest in your efforts to monetize your content.