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Senator John Fetterman 's recovering after his nasty fall ... sharing a picture of his face after needing stitches to sew up his wounds.

The Pennsylvania representative posted the selfie to X Saturday morning ... saying he's back at home with his wife, Gisele , and their children after being hospitalized and getting 20 stitches. X / @SenFettermanPA

In the pic, Fetterman's got healing cuts on his nose and one large gash above his right eyebrow ... though he's got a big smile and an iced coffee in the photo, too.

Fetterman thanks everyone for their well-wishes and his doctors for their excellent medical care ... and he promises he will be back to work in Washington, D.C. very soon.

ICYMI ... the senator was rushed to a Pittsburgh hospital Thursday after he f

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