Hello and thank you for your question. I'm sorry to hear that you aren't feeling well.
Your worsening sore throat and vomiting sound very much like strep throat. This is a bacterial infection caused by streptococcus that is contagious. It is very possible that you acquired it from your kids. You may also develop a fever with this type of illness and, in more severe cases, a "sandpaper"-like rash on your chest or back.
Although your doctor's office is closed today, you should definitely make an appointment to be seen tomorrow. Most doctors have a rapid test for strep in their office which can confirm the diagnosis. The infection responds well to penicillin-type antibiotics. Untreated strep infections can lead to serous illnesses such as rheumatic heart, so it is important to get treatment.
If you end up with a negative test for strep, the other possibility is a viral throat infection. One that is associated with increasingly severe symptoms is the Ebstein-Barr virus or mononucleosis. In this case, the sore throat would last longer than 5 days and be associated with fatigue, abdominal pain, and fever.
Until you are seen by your doctor, I would recommend taking ibuprofen for the throat pain and drinking plenty of clear fluids.
I hope this helps. Feel free to ask additional questions when you return online.