Cara underwent microlaryngoscopy and bronchoscopy along with flexible bronchoscopy by the pulmonary department and bilateral myringotomy tube placement.

I struggle with capitalization... Is pulmonary department capped? Thanks

Not usually, but if the specific medical center or hospital capitalizes the P and D, then you would. Since you don't know, then leave them uncapitalized.

http://grammar.ccc.commnet.edu/grammar/capitals.htm
See #4 here.

You also need commas after both instances of "bronchoscopy" because "along with..." is a parenthetical phrase.
http://grammar.ccc.commnet.edu/grammar/commas.htm
See #4 here, too.

When it comes to capitalization, there are different rules that apply to different situations. In this case, "pulmonary department" would not typically be capitalized unless it is a specific department with a formal name, like the "Department of Pulmonary Medicine" or the "Pulmonary Division." In general, when referring to a generic department or job title, it is not necessary to capitalize it. So, unless the department is explicitly referred to with a formal name, you would write it as "pulmonary department" in this context.