What can it be ?

I have a 4 year old step son and I've never had him while sick until now. The mom is being ridiculous and won't let me take him to the doctor and she won't take him herself. He's fine most of the day with the exception of a cough, but what concerns me it's that he's been throwing up. I only have him weekend so Idk what goes on at her house but for the past 3 weekends he has been throwing up once a day. I'm starting to get worried that it might be something other than a cold. What can it be? I'm not sure how to help him without going to the doctor bc she just won't collaborate.