The terms digital fingerprint and ordinary computer are rather vague descriptions. It depends what you want to reach. Communication over the Internet is IP-based, so a server can at least see the IP address of a client trying to communicate with it (you!). If you are communicating with a web-server over the HTTP-protocol, i.e. browsing, more information might be revealed to the server, e.g. cookies.
If you want to bypass geo-blocking, you have to first find out how the target blocks foreign clients. Usually it boils down to IP Blocking: used by services such as BBC iPlayer, this method compares your IP address with a list of known addresses (associated with a country) and decides whether to block or not.
To circumvent IP-Blocking you could use a VPN service. But beware that services also stay up-to-date and might block known VPN-addresses. Choose a VPN-Provider which regularly updates/changes its addresses.
1What do you mean by data when you saye "it changes your data"? IP-Address? Cookies? What exactly? – Yan Foto – 2019-05-08T09:21:09.513
Tor mainly changes IP address regularly. Otherwise, it looks like any other Tor install (unless you do something to make it look unique). Tor is detectable, even if you could force it to always exit from the USA. Most commercial VPNs are detectable, as are server farms where you might run your own VPN. How sophisticated the destination site is at detecting these situations is an open question. Can you do any probing with a fake account to test it? – pseudon – 2019-05-08T12:49:40.263