Keeping relative time (simply) without RTC

That's fine, only rarely is a clock actually needed, but, in the absence of posted code it is hard to tell what you do care about. Guessing that your loop is a minute long, all you need do is include a ++ count and send that as data. Also, since it seems you are connected to PC, you can use a kosher terminal that not only records the data but also timestamps each package received, using the PC clock. Terminals, like RealTerm, Putty etc., all do this and all are freebies. You can also send the data direct to Excel, and stamp that with an Excel command. In these instances, the timestamp is the full bottle, but that doesn't cost any extra, and may even be useful.