I keep goats and sheep sometimes in the same fields and sometimes rotating separately depending where the grass, nettles and hedges need eating most.
They mostly stay in their own groups and don't cause each other problems even the big rams and bucks.
Goats don't build up the same tolerance of worms that sheep do so will need to be dosed regularly or yes you will have problems.
You do know that the goat dose has to be higher than for sheep. Some wormers twice as much, some one and a half times.