"I enter the hospital."
I think that the person is outside yet, because s/he says 'I enter the hospital'.
The image of imagination is 'to' or 'toward' the hospital.
わたしは病院を出ます。 I leave the hospital. (sorry, please offer more better English sentence)
This person is in the hospital. I think the image is 'from' the hospital.
And the particles are different as the same the meaning of each English sentences.
Hairi はいり and iri いり are both readings of 入り。tried to find a good rule for when to use each and found this. https://www.lingq.com/forum/learning-japanese-forum-ask-a-tutor/iru-or-hairu/