I applied for NHS with GPA of 3.8 which is not very high but was definitely above the requirement of 3.2.
Im pretty sure I did everything right but just not getting any messages or emails back.
Am I denied…?

Your HS will have an NHS advisor. Ask them the schedule for NHS. usually it is at the end of the year. Also you cuold talk to your Guidance Counselor.
Some NHSs have requirements for service as well
I am pretty sure you have to have tens of hours of volonteering to get accepted in NHS.
^I had like 300 hrs
Has your school already had inductions? Some do it in the spring.
Each school is responsible for its own NHS membership. (I"m moderator at my school.)
And know that it takes hours to go through the criteria for each and every applicant-- it’s entirely possible that your name simply hasn’t hit the top of the list yet.
Sometime today, go to the moderator of NHS, and ask whether there was an error.
I found out they were still adjusting things! Today, I was walking the hallway and found a sheet of paper with NHS on it with a list of names, and my name was on there too. So I guess I’m part of it,
but still not sure why they didn’t call me or anything 
I know that my school admits ballpark 300 new members each year-- we’re a big school!
In addition to my duties with NHS, I also have 5 Precalc classes and a homeroom, as well as a study hall.Then I go home to be mom to 3 teens. I don’t have lots and lots of free time.
And what would they have called you to say? “We’re still working on the applications”??
Hang in there… they’ll finish the process when they can.