I can't get a medical consultation because the hospital in my neighborhood is closed due to the New Year's holiday.
ご質問ありがとうございます。
"I can't get a medical consultation"=「受診できません」
(*medical consultation*はややフォーマルな言い方なので、*I can't see my doctor*=「主治医に会えない」とも言えます)
"because the hospital in my neighborhood is closed"=「近所にある病院が閉まっているので、」
"due to the New Year's holiday."=「正月休みだから。」
ご参考までに。