From stackexchange: (https://japanese.stackexchange.com/questions/66781/to-see-a-doctor_

As an aside, 見る can be replaced by 診る(in 見てもらう), the majority of people use 診る in this sense, but I don't think 見る is wrong. Two dictionaries I checked say （「診る」とも書く）

「病院を」でもOKですか？「病院で」ではなく – sazarando Apr 24 at 5:42

@sazarando 病院で見てもらう is fine, but 病院で受診する sounds tautological and weird to me. 病院を受診する is fine, but 病院を見てもらう would mean "to have someone look at the hospital". – naruto Apr 24 at 7:24

見てもらう
    Context-wise, this word is likely used when you are already focused on (care about) a specific symptom you have, such as "I have an unusual headache, so I'm going to see a doctor" or "I have a such-and-such chronic disease, so I must see the doctor every week". That's because it literally mean have it seen (= diagnosed, treated).

受診する

受診 can take an institute name as a direct object.
Although it's a single word to mean "see a doctor", the term is not a very casual word, say, for a child to use. Of course, it is okay for whoever an adult to use it in conversation, just always sounds like "ophthalmologist" instead of "eye doctor" (I hope I didn't misspell).

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私は病院を受診する。    (from weblio)
I get a check-up at the hospital
*受診する points out to the series of actions:'病院へ行って、診てもらう'
 (from: 「で」か「を」かについて考えるなら、これは単に文脈の問題という気がします。「病院へ行って、診てもらう」の一連の行動を指す言葉として「受診する」を用いるなら「○○家を訪問する」のように「を」を、「診てもらう」事だけを指すなら「○○家で会食する」のように「で」を使う事になるのではないでしょうか。

そして医療関係者は病院あるいは診療科の外から患者が「来る」感覚が一般的に付属するので、自然に「を」になるのではないか……などと思うのですが、いかがでしょう。
(And,for the medical staff, since the patients come from 'out' of the hospital, it feels more natural to use を)
 from:http://natrom.hatenablog.com/entry/20070719/p1)
*を:shows place where action occurs, this を　is similar to 家を訪問する(visit a house) or ヨーロッパを訪問する
*受診する:(intransitive verb) to recieve a medical examination from a doctor
IT CAN BE USED AS IN "GO SEE A DOCTOR, GO TO THE HOSPITAL, GO TO A HOSPITAL DEPARTMENT(産婦人科って受診=Going to ob/gyn)
BUT IT REALLY MEANS "GO TO THE DOCTOR/HOSPITAL/H.DEPARTMENT(FOR EX. OB/GYN) AND HAVE THEM EXAMINE YOU
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病院を受診する: More common
病院で受診する: Not wrong but less common
病院で何科を受診するんだよ？: Feels weird somehow
内科で受診する: Subjectively speaking Feels very wrong
××先生で受診する: Feels absolutely wrong
××先生を受診する OR ××先生に受診する: Feels right
(Ex: 片頭痛で〇〇医師を受診したら、私の保険がどれだけ適用されますか？
     If I see Dr. 〇〇 for migraines, how much will be covered by my insurance?)