I work at a very busy veterinary clinic. Our schedule for normal appointments is typically backed up about three weeks, but we do squeeze in emergencies and not-quite-emergencies-but-can't-wait-
that-long appointments for our regular clients, and sometimes for new clients. Often we get calls from people who don't have a regular vet and/or have never taken any animal to a vet, and we can't help them all.
I became a vet tech because I love animals and want to make a difference in their lives. It hurts to not be able to do that, but there are only so many hours in a day. It's frustrating because so many people lay guilt trips on us, when it's not
our fault they never bothered to establish themselves with a vet. They'll say stuff like "can't you just fit us in at the end?" without realizing that we have often already put in a ten to twelve hour day, and are tired and hungry. We're human. At the end of the day, we just want to go home and spend time with our own family and pets.
Also, it's annoying when we do try to squeeze someone in, and "that time just doesn't work," and, again, expect us to stay open even later to get them in at the end of the day. If this was your sick child, you'd make it work. If you needed to get to a store before they closed, you wouldn't call them up and expect them to stay open an hour later just for you.
To make a what-was-supposed-to-be-a-short-rant short, develop a good relationship with your vet before problems arise. Don't wait for an emergency to happen. It doesn't take much to be seen as a good client in the doctor's eyes. Show up on time, preferably a little early. Keep scheduled appointments. Don't cancel at the last minute or fail to show. Pay your bills and don't bounce checks. Just be respectful and responsible.
(Just so no one thinks we're totally cold-hearted, there is a local emergency clinic that's open 24/7 with no appointments necessary. If we can't get someone in, we always give them the number for the emergency clinic. Unfortunately, a lot of people don't want to bother going there because it's about 20 miles [mostly major interstate] from the clinic where I work. To some people, that's like asking them to fly to the moon.

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