I had a similar situation last year, I searched the internet for a "good plumber near me", but there were those who didn't pick up the phone, or promised to come "in three days". Finally found a plumber near me and didn't regret the choice. You can go to their website, it describes what types of services they provide and approximate prices. If someone also does not want to risk with “random” masters - I advise you to look at their website. There, it's clear what kind of people are behind the service. And, by the way, they do not only emergency calls - you can order a routine inspection. I renewed my entire bathroom in this way - calmly, without nerves.
I had a similar story a couple of months ago - it seemed like a small thing, but in the end I had to turn off the water in the entire apartment. Since then, I prefer to call a repairman right away. It is better to look for those who have reviews on the Internet or who work through trusted services - there are now many aggregators where you can at least see the rating and real experience of other people. And yes, do not hesitate to ask the repairman in advance how much the work will cost - this often saves you from "surprises".