Although a lab can process a specimen in a matter of minutes, from the time you give that specimen until you hear/see the results can take days. If your results are released to you directly by the lab doing the work (e.g.: via a web portal or EHR), you may get them within a day. If your results have to be reviewed by a physician first, then it may take several days, and in some cases, you have to call them to find out.
I agree about the communication issues and planning. I'm currently helping my mother with her treatment for pancreatic cancer. We are routinely calling the offices of her doctors, looking up results online and getting them well ahead of the treatment team, and finding errors (even egregious ones) in her lab work or even discovering that no one told her about important issues.
Perhaps you can talk to the practice manager at your doctor's facility and arrange to have direct access to your blood work results. I've had some success with that approach.