Entering input causes modal reloading automatically

It seems like you're declaring your hooks outside your component. Try putting them inside your ReturnModal function instead, like this:

const ReturnModal = () => {
  const [price, setPrice] = useState(0);
  const [shippingCost, setShippingCost] = useState(0);
  ...

Documentation reference: Using the State Hook.

Also, I would strongly recommend using the React Hooks ESLint Plugin (among others) to detect issues with your hooks. Here is a guide on how to add this to your React Native project: Add Eslint Support to your React Native Project + React Hooks Rules.