Tang Ho has basically answered this already, I’ll just give what I have.
临床 is the same as the English bedside as in bedside manner of doctors.
东床 is explained in A Chinese-English dictionary as:
eastern bed—son-in-law (from an anecdote about the celebrated calligrapher Wang Xizhi 王羲之 (321-379), who as a young man remained eating bare chested on the eastern bed when an official came to choose a son-in-law for the minister's daughter, and who was selected for his independence of mind over his well-behaved brothers)
a good son-in-law
So, yes, as you said 床 just means bed.