Basically I filed independently on 4/13/2020 and my Mother filed on 4/16/2020. Last year I was her dependent but this year she did not claim me as a dependent. Will I get the stimulus check? I was thinking I May miss out on the check because the taxes were completed so late and my mother already got her stimulus check before she completed the 2019 taxes.
As pointed out in the comments, the question is not did she claim you, but could she claim you for 2019? If she could claim you for 2019 then you are not eligible.
There are other rules, but usually if she pays more than 50% of your living expenses then she can claim you. You said in the comments that
I lived with my mom always at the same address and she does pay for me with the exception of me paying my car and insurance. I am a college student and am 19 right now.
Assuming she pays for the mortgage/rent, utilities, food, tuition, etc. then she is probably paying more than 50%. You should have checked the box that someone could claim you, and she should have claimed you.
Either way, you are not eligible for the stimulus check, regardless of what your mother gets. You might still get a check since you incorrectly stated that no one could claim you in 2019, but the IRS prefers that returns be true and accurate. I don't think the IRS would make you pay it back, but they could flag your return for being incorrect.
You can file an amended return to fix it, and your mom might want to file an amended return as well and claim you for the tax benefits. She will not get the $500 stimulus since you are over 16, but she still gets other credits.