Burps smell like vomit and gross toots

So my son had the stomach bug bad. He’s still getting over it but is back to wanting to eat and drink normally. His burps smell like vomit and sometimes I can tell he does throw up a little. He also has the stinkiest farts the past two days. Like to the point I’m gagging. Has anyone’s baby had the stomach bug pretty bad before? Did this happen? I’m going to call his doctor Monday but knowing them they’ll just say he’s been sick he’s fine! Should I push for him to be seen though?

He’s 13 months. Thanks!