Do you think you have it from the encounter you talked about a year ago? Have you had any other symptoms?
Let's say you do have it. Let's start with transmission.
You are only infectious from the site of your infection. If you have oral herpes - cold sores - you are only contagious from your mouth. If you have genital herpes, you are only infectious from your genitals.
This means that if you only have genital herpes, you can kiss your kids with no worries. If you have oral herpes, you can kiss your kids on the cheeks with no worries. The skin on cheeks is too thick for the virus to penetrate.
It's thought that sharing drinks will not transmit herpes, but because chapsticks stay moist, that might.
With colds, flus, strep, covid, etc., it's a good idea to teach your kids that sharing drinks and chapsticks and such isn't a good idea anyway, and that can start with you modeling that.
If you have genital herpes, you are only contagious if your unclothed genitals come into contact with someone else's unclothed genitals with friction. This means that if your kids get genital herpes from your genital herpes, you've had inappropriate sexual contact with them.
Herpes, and other STIs, do not go through clothing. If your kids are sitting on your lap, you can not give them herpes.
Now, why haven't you been to the doctor? Almost exactly a year ago, you had irritation, and no risk for herpes. If that's your only concern, and you're still having symptoms, you really need to see a doctor to find out why you are having symptoms.
If you're in the US, and lack of insurance is a concern, go to a local Planned Parenthood, your local health department, an STD clinic. Just please go see a doctor.