There are a lot of factors with kidney stones. Size is important, and often, if the size is too big to pass on your own, doctors will pre-emptively schedule treatment to resolve this so they do not lodge and create backup issues with the kidney, which can damage it, cause infection and even more serious issues.
I'm taking that the doctor was not concerned on the size then, if this did not occur. Certainly, if he/she was, then they would have recommended you see a urologist.
It also sounds like this is the first time you have had this issue, so it does not seem to be a repeated problem that you need to do some analysis to determine what type of stone it is. There are many types . .. some are calcium oxalate, which there are various theories of root cause . . . some are uric acid based . . . and others.
Generally speaking, no matter what type of stone, it would be well-advised to avoid substances and behavior that would "dehydrate" you . . . such as alcohol or just failing to drink enough water.
If you have anxiety about this situation, and it sounds like you do, contact or setup an appointment with your practitioner. Some will advise that you just drink a lot of water for a period of time to see if this can help move things along, especially if the size is small enough. It is possible to pass kidney stones on your own, and certainly there can be varying degrees of pain, but it is done. There are also other, less invasive procedures, that use radio-frequency waves to blast the stone into smaller pieces to make it easier to pass, and then finally, one can have them removed manually, but this does not typically require "cutting open" a person's kidney.