A painful point about hospital that’s stranded? (6)

I believe the answer is:
ashore
'stranded?' is the definition.
(I've seen this in another clue)
'a painful point about hospital' is the wordplay.
'painful point' becomes 'sore' (I am not sure about this - if you are sure you should believe this answer much more).
'about' means one lot of letters goes inside another.
'hospital' becomes 'H' (abbreviation for hospital).
'sore' going around 'h' is 'shore'.
'a'+'shore'='ASHORE'
'that's' is the link.
Can you help me to learn more?
(Other definitions for ashore that I've seen before include "Hoarse being no longer at sea" , "On land (as opposed to the sea)" , "Hoarse (anag)" , "Toward land from the sea" , "Aground" .)
