The standard way how to tell the PC "I am full, please stop sending data" is to use handshake.
If you use hardware handshake, you need to add an extra line from the mcu to PC (connect to "CTS" at PC).
If you use software handshake, send XOFF/XON characters to PC to make it stop/start sending data. In this case you must make sure these characters are not occuring in the data you are sending (e.g. this is fulfilled when sending data in intelhex format).
In both cases you need to buffer the incoming data, as the PC might send some extra bytes until it stops.

Of course you can also make up your own protocol, but if you use standard methods you can use standard tools (e.g. terminal emulators) to upload the datafile.

Jan Waclawek