In some respects, to potentials that dont know you might think that your org isnt legit because its not a "panhel" org, but in other respects, there are potentials that have no clue what "panhel" even means, so youre fine. I dont think it really matters. You will always kind of battle that issue, but in the end, I dont think it will hurt you much.
As to forming a national council of locals....that doesnt make sense
but that wasnt in the original question....so I am moving on....
I agree with whoever said "just act legitimate". I mean, youre a local, you dont have a national, but it doesnt mean youre not operating as a sisterhood! Present yourself professionally, be organized, show pride in your org and I feel like you'll be just as legit as the other organizations on your campus. (I would suggest that you probably already ARE legit, but maybe your group doesnt feel legit because of the lack of national thing? So just have confidence!)