This saying refers to an individual who is not in a stable situation themselves, and worries about other people's problems. Please give me the English/American equivalent.
My first inclination was to quote the Bible which has the phrase "You hypocrite, first take the plank out of your own eye, and then you will see clearly to remove the speck from your brother's eye." -Matthew 7:5, but there's also the lyric from Elvis' hit, Clean Up Your Own Backyard.
Put your own oxygen mask on first (before helping others).
It is a saying adapted from pre-flight safety instructions and used as a metaphor like OP's phrase. It is self-explanatory. You should help yourself first before helping others. (which also implies that you might not be in a stable situation yourself.)
An example article that mentions this metaphor:
As FumbleFingers suggested in the comments, "Charity begins at home" is a common phrase that comes to mind but it doesn't meet certain criteria:
It is not about individuals, not about "self-care", it is about helping people close to you. Also, it is mentioned that it is frequently misused: http://www.cracked.com/article_20251_the-5-most-frequently-misused-proverbs_p2.html
It doesn't imply that you are an individual who is not in a stable situation. OP's phrase and the phrase I mentioned both have that sense.
Martin Manser, The Facts on File Dictionary of Proverbs (2002) has this entry for the saying "Physician heal thyself":
physician, heal thyself Do not reproach another person for something that you are equally guilty of; also used to imply that you should solve your own problems before you try to deal with those of other people: [citations omitted.] The proverb is of biblical origin: "Ye will surely say unto me this proverb: Physician, heal thyself: whatsoever we have heard done in Capernaum, do also here in thy country" (Luke 4:23).
Note that this saying can be used to advise that "you should solve your own problems before you try to deal with those of other people"—which is essentially the same recommendation that U.S. airlines make with regard to oxygen masks in their pre-flight instructions (cited by ermanen in another answer). The Facts on File dictionary also offers this saying:
if every man would sweep his own doorstep, the city would soon be clean If people made an effort to improve their own behavior, instead of criticizing other people's, the world would be a better place: [citations omitted]. The proverb was first recorded in 1666, in an Italian proverb collection, but the sentiment it expresses is of earlier origin.
Another anglicized proverb comes from the final page of Voltaire's Candide (1759), where the hero says in response to a philosophical musing by Dr. Pangloss: "All that is is very well, but let us cultivate our garden." This conclusion yields the idiom (in English):
Let us cultivate our [or our own] garden.
a literary character comes to mind - Rip Van Winkle