3 Year Old Vomiting , 140 Bpm
Take her to Emergency immediately
Detailed Answer:
Hi
I have gone through the query and do understand your concern.
Frequent vomiting itself may cause dehydration and if severe may lead to shock.
Sleeping heart rate of 140/min is abnormal for this age and may be due to severe dehydration with hypotension/shock or some myocardial issues.
Letharginess is also not a good sign.
I suggest you to take her immediately to Emergency for clinical evaluation and management like intravenous fluid supplementation if needed.
Wishing good health for your baby
Regards