1. I went to see an otolaryngologist
to have my hearing examined.
2. I went to an otolaryngology to
have my hearing examined.
3. I went to an otolaryngology
hospital to have my hearing
examined.
4. I went to see an otolaryngology
doctor to have my hearing examined.
5. I went to see an otolaryngology
specialist to have my hearing
examined.
(Which expressions are grammatical? Are all OK? Can we use 'checked' instead of 'examined'?)
#2 is not correct. The "ist" on the end of the word indicates a person. The "ology" on the end of a word, indicates an area of study.
For instance a musicologist is a person who studies music. Musicology is the area of study.
The rest are good! You definitely may used "checked" in place of "examined".