Lyric discussion by brumus 

Cover art for Third Week in the Chelsea lyrics by Jefferson Airplane

It is about contemplating the break up of Jefferson Airplane (not Starship) from the perspective of Jorma Kaukonen while staying at the Chelsea hotel in NYC. Jorma had thought about leaving JA since 1968 and by 1970, with HT going, he wanted to move on.

"Straining every nerve" line refers to trying to keep up the image of a counter-culture rock band when that dream was fading fast.

The line "So I walked into a little room that whistled like a sigh" is about walking into a room with one of those old steam radiators for heat that make a noise and that are found in older buildings like the Chelsea.