Deleting and Adding Custom Fields
I do not think it is because you have too many custom fields but it might well be that something is not totally right in your data? Ideally you should compare the values in the civicrm_custom_group and civicrm_custom_field tables with the actual data holding tables (in your example civicrm_value_care_init_69) and check if that is all correct.

The error also suggest that there is a constraint, so you probably use a field type of contact entity reference somewhere? And perhaps that is not entirely correctly configured? It is hard to be sure with only the error message to go by :-)