From the context and his join date, the OP is probably referring to "Lisa's Simple C" Poundhound, not first form aka Open C. Causes regular communication confusion here.

peterjohnston887 Hi. welcome to the forums ☺

Acoustic or electric? I'll surmise acoustic.

[u]"Buzzing" on the 1st string[/u]. Take your fretting hand away and pick just the high E string. Does it still buzz? [u]If it only occurs when you are fretting the B string for 'simple C'[/u], the cause is almost certainly your forefinger inadvertently touching the E string whilst you are fingering the B string.

Otherwise, a buzzing string can be attributable to numerous causes. Is the guitar new? If not, old strings - change them. Often as simple as that with E string buzz. Alternatively could be poorly cut or worn nut, damage or just action. Take the guitar to a luthier/store and have someone check neck relief for you. If it's not a new guitar, other fret condition/level. That covers finger trouble and guitar trouble.

Nail interfering with G string. A. Trim all the nails of your fretting hand extremely short regardless. B. Pay attention to placement of your forefinger on the B string forming your hand and curling your finger so it doesn't inadvertantly touch either adjacent string. G or E.

Expectations. You've been at it "a day". How many minutes/hours actual hands "practicing" in that "day"? That chord as illustrated by Lisa is easily accomplishable within "a day". [u]Rewatch the lesson, pay attention to finger form so as to avoid touching adjacent strings in fretting the B string[/u].

No nothing to do with "finger toughening". Similarly even small hands short fingers won't present an obstacle to fingering this chord as illustrated by Lisa.

Try again as advised. Persistence is one of several quintessential temperamental characteristics to nurture to progess with guitar.