Friend, a dog's normal temperature is between 99.5-102.5 F; ours is 98.6 F. So, upon touch a dog will always feel warm to us, the only way to rule in a fever is by taking a rectal temperature.
When a dog is unsteady on their feet this could be a sign of a systemic disease or neuromuscular disorders. The fact that he was vomiting and straining I am inclined to believe this could be related to a systemic disease. Possible causes are: Pancreatitis (inflammation of the pancreas), liver or kidney disease, ingestion of a foreign body, etc. to name a few causes. The panting could be a sign of discomfort, fever, heart disease, etc.
Unfortunately in this case we are somewhat limited as to what you can do at home. Alfie's treatment will be dependent on underlying cause. In order to determine the exact underlying cause he will need a hands on examination by a veterinarian, blood work and xrays as initial screening test. In the meantime you can start him on Pepcid AC (famotidine) 10mg 1/4 tablet every 12 hours or Zantac (ranitidine) 75mg 1/4 tablet every 12 hours; you can buy this over the counter in any pharmacy (chemist). Continue feeding him a bland diet of rice with boiled boneless chicken or ground beef. Follow up with a veterinarian as soon as you can.
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