It's not uncommon for small breed dogs like chihuahuas to have a delayed onset of soreness from vaccines and even a reaction to them. The drooling itself can be due to pain, anxiety, nausea, etc. Having eaten some beef, yes, this could very well be causing her to feel unwell. I, personally, would expect that this is due to nausea from the beef. If she does not improve by morning or worsens overnight, please have her examined.
If she is unwilling to eat at this time, this may indicate an upset stomach. You can administer a dose of regular pepcid (famotidine) every 12-24 hours. You will want to give 0.5mg/pound of body weight (a 10# ***** would receive 5mg, a 5# ***** would receive 2.5mg, etc). For this, you can visit any human pharmacy and buy the OTC brand name Pepcid, or you can use the cheaper, off-brand “famotidine” that’s available. Either will be useful.
If she is eating but lethargic this may be due to soreness or a reaction to the vaccines. You can give 1-2mg/pound of body weight of benadryl every 8-12 hours. For soreness, it would be ideal to have her examined by your vet and canine-safe NSAIDs given. In a pinch, we can use aspirin too. Dosage here: http://www.veterinaryplace.com/dog-medicine/aspirin-for-dogs/
If she was recently vet checked, it's unlikely that she has anything to pass on to your children. We become primarily concerned about intestinal parasites, which most vets check for during routine vaccine visits.
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