The IP address provided by my ISP changes. I want to know if it is shared by someone else in this world.
If the ISP is using CGN (Carrier-Grade NAT), it is possible that the IP address assigned to you by the ISP is the same address as the ISP assigns to someone else in it's network, and another ISP could use the same address in it network.
If the ISP is assigning you a publicly routable address, it is unlikely, but not impossible, that it is reusing that address elsewhere, but it would need to be using CGN with publicly routable addresses in that case, and that is very unlikely.
CGN is for conservation of publicly routable addresses, and the ISP can use non-routable addresses for that, conserving any public addresses it owns for those willing to pay for that.
Of note is the fact that the RIRs have run out of publicly routable IPv4 addresses to assign to the ISPs, which are now implementing CGN in order to conserve their existing publicly routable addresses for those willing to pay extra for that privilege. This is causing problems for the ISP customers because that breaks things since the ISP will not forward ports across the NAT the way in which the customers have been doing.
RFC6598 defines 100.64.0.0/10 as prefix for Shared Address Space. If you get an address from this prefix you are very likely behind a provider based NAT. Same is true for addresses from RFC1918 prefixes (10.0.0.0/8, 172.16.0.0/12, 192.168.0.0/16). Providers may also use public address for shared addressing.
You can test if you are behind a NAT by using websites like this (Looks like it's no working right now.)