unfortunately you aren't able to see since when the interface is up. Via "show int ..." you can see how many packets, errors etc were received on the interface since the last time these counters were cleared. For troubleshooting purpose you can manually reset those counters via "clear counters ..." So the counters have nothing to do with the uptime of the interface. Your only chance are some logfiles were you may be able to see up/down messages of the interface.
Topology changes are normal and shouldn't have any impact on your network if they aren't massive. A simple switch failure, link up/down event could cause those changes. Just ensure to configure your ports correctly (Portfast, BPDUGuard, Prioritiy etc)