Stomachaches are not contagious, but they might be in the future in the form of a Stomach Flu (this will be linked to Burning Belly in GTW version). How toddlers feel about their illness symptoms depends on their trait, most will be sad, but Wild, Fussy, and Independent will become angry from their symptoms instead.
So my toddler is sick, now what?: Sick toddlers are given a broadcaster that can spread to other sims (only other toddlers if you do not have SOL or GTW installed), there are different broadcasters depending on if they have the flu (older sims get Llama Flu in GTW version) or a cold (older sims get Triple Threat in GTW version). There is, however, an extra way I made for testing and cheating: a pie menu for selected toddlers that will make toddlers sick instantly with a Cold, Flu, or Stomachache. **NEW** They can also get sick from being away at daycare through either normal gameplay or in LMS’s daycare activity. Getting a toddler sick is pretty easy: similar to KawaiiStacie’s Slice of Life mod, toddlers will get sick the same way older sims can: poor hygiene, eating too much food, eating bad food, other sick sims, the weather, or just because, with similar requirements so it’s not too foreign for SOL users.