On Changing currency its showing the default currency after Proceed to Checkout

Hi Team,
Our Store address is https://ecoaurous.com/
Currently we have 2 currencies available to the website
1: INR for india
2: USD : For other countries

For this we have implemented 2 links with flags above to the website Main Menu Bar.

1: We have tested that if you choose India On SELECT COUNTRY
2: It Will show you the INR Rates up-to the cart page but when you click on the Proceed to checkout page, Its showing the default currency which is USD
So all the prices are showing differently.

Its really helpful if you check on this issue