Its nose is dry and cracked with some peeling, appetite is okay, it doesn’t like to move — maybe the hind legs keep trembling and it can’t walk far. Sometimes it vomits.

A dry, cracked dog nose can be caused by high outside temperatures, insufficient water intake, a cold or fever, or other illnesses. Judge the cause from the actual situation; if it is from a dry environment, apply some moisturizer and give the dog more water. If the dog has a fever, provide physical cooling or fever-reducing medicine promptly.

In addition, based on your description the dog also shows vomiting and trembling, so in this case take it to a veterinary clinic for a thorough examination and targeted treatment based on the results.