Hey,

I believe there is no such thing that you can't do a BSC degree after three years of gap untill the college you want to take admission in specifically mentions that.

You can easily pursue your Bsc in nutrition form any college after completing you BA. People do take gap from studies and then rejoin college after two or three years of gap.

Just fill the form of college you want to take admission in and then if you qualified for admission you are good to go.

Hope that helps.

All the best.

Thank you.