Caring is wrong?

Is caring is a bad thing according to Buddhism ? Because as I experience caring leads us to suffering. But caring can come in so many levels such as we do help a person normally as a result of our caring towards that person/ animal. And in a relationship we do caring on very tiny things even by checking the other person has reached home safely etc. But in the big picture finally we get reasons to suffer due to our caring. It seems like we can get rid of most of the sufferings if we do not care. So is it not appropriate to care ? Otherwise how can we avoid suffering ourselves while caring ?