The wormer Cydectin does not have a slaughter withdrawal. It should get rid of them. We also spray with a concentrated permethrin - it also works.
We have ticks pretty bad in our native grass pastures. They don't get on the cow's body too bad with once a year worming, but we usually spray the ears on cows once a year to make sure they don't get too bad.
I'm surprised they made your calf sick that quickly? Are you sure that wasn't something else. Ticks are just more of a nuisance.