Hey @KadriValentiina ,
Welcome to the Shopify Community! Happy to have you here.
From my understanding you want Estonian to be your main language, but to still have English available. The best option will be to swap the languages; have Estonian be your theme language and then use your translation app for English.
Although I understand you didn’t want to go that route, it would require you to change the theme language manually. If you go with this, our Translating themes help doc will explain how to do this.
Alternatively, you could contact the developer of the translation app you are using or check out any help documentation they have to see if there is an option to set a default language. Their app might be able to override the theme language and immediately show your shop in Estonian instead.
You can contact the app developer from your Shopify admin by going to Apps then clicking Get Support across from the app name. They’d be able to help you out and confirm what features you can leverage from their app.
There is also the option to use International Domains. This feature is available on the Shopify plan ($79USD) or higher. It would allow you to utilize subdomains for different languages, for example en.yourdomainname.com for your site in English and ee.yourdomainname.com for Estonian. This would be another good option for you.
Let me know if you need me to clarify anything!