Can I change my iTunes Store to the American store?

Not really. You could but it would be against the terms of use of Apple's media services, and it would also be very difficult to do without moving to the USA and setting up a bank account here.

http://www.apple.com/legal/internet-services/itunes/us/terms.html - "Our Services are available for your use in your country of residence (“Home Country”).

Change your Apple ID country or region - https://support.apple.com/HT201389

Only if you're in the USA and have a payment method valid there. A gift card cannot be used to change iTunes Store countries.

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I don't see where the OP asks about a gift card.