Not all animals get nauseous with oral antibiotics, and a majority of those that do can eliminate the nausea when food is given with or before the antibiotic. But, there are some that have the nausea regardless.
Re the 10 day antibiotic shot, there are places where this is preferable especially when giving the antibiotic is impossible due to the animal's behavior. One thing to consider, if there is a reaction to the shot, the meds are in the dog/cat for 10 days, there is no way to eliminate it. With a pill or oral Rx reaction, the 1/2 life is hours and the drug is usually out of the body within a day or two.