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Not usually. This is often just a sign of dominant behavior. I suggest that you start an obedience class with him right away so that he will learn that you are the alpha. Once you teach him to sit, make him sit for meals and for treats.
Dogs like this need special care.
Keep in mind that kennel cough and respiratory infections will often clear up on their own BUT if you see green or yellow snot, you need to see the vet for antibiotics.
Let me know if you still have questions.
If he only does it when you pick him up, it could be aggression. Most aggressive dogs do not like to lose control.
In situations like this, you should always see the vet to rule out a medical reason for the behavior and then begin training if that proves false.
Let me know if you want to discuss this more. This is my area of expertise.
These little dogs are known for their tempers so I suggest that you go all the way through canine good citizen with him.
Dominance down is great but the dog needs the basics, too. You also need to use the Nothing In Life Is Free theory with him. Make him sit before you take him out. Make him sit for water. Make him sit for everything. The more you make him work, the better the relationship will be.