In those days doctors ladled across antibiotics to patients.

• The improved sentence: In those days doctors ladled out antibiotics to patients.

• ladle something out (phrasal verb with ladle verb)
English Meaning: to give money or goods in a (too) generous way to a lot of people.
Bangla Meaning: হাতা দিয়ে তরল খাদ্য বিতরণ করা; ঢেলে দেওয়া।

Source:
1. Cambridge Dictionary.
2. Accessible Dictionary by Bangla Academy.