Will I get a penalty if I was insured under my mom most of the year but not the whole year?

[hbl3973]

Possibly.  But there are quite a few exceptions.  The instructions for IRS Form 8865 (https://www.irs.gov/pub/irs-pdf/i8965.pdf) give the list and their details.  Look especially at the first three listed on Page 3 of those instructions.