Medical exception

Can someone help me find info on medical exception, rather than religious exception to avoid childhood vaccinations? My cousin lives in West Virginia one of two states which has no religious exception. She is helping raise her daughter's two little girls, the youngest of which was very sick just after her last vaccination. She seems to have lost what speech she had so far attained.

They live in a rural area, and if they are to avoid vaccines, they will have to have everything together before approaching a doctor.