No, if you started in May and the 2016 summer was in the prior FA year (which is normal), I think the June 30 date is just the deadline to apply for the prior FA year (or for the school to disburse the funds). This summer, 2017, is likely part of the 2016-17 financial aid year. The fall will start your new FA year.
I think you are getting a Pell grant in each semester. Most students do ‘use up’ the Pell grant half in the fall, half in the spring so there is nothing left for summer. I think that’s the position you are in now. Look at your FA award from the fall and spring. Is there a line for Pell grant?
It is likely there is nothing left for the summer from your 2016-17 financial aid pot. That happens at MANY schools, to many students receiving FA. My kids use all their aid in the fall/spring, so haven’t been able to take classes in the summer. If they went in the summer, we’d have to pay 100% for it out of pocket as they have no grants or scholarships left for the summer. If a student hasn’t borrowed the entire amount of the direct loan, that could be borrowed for the summer.
It sounds like you used all your FA for 2016-17, so didn’t have anything left for this summer and that’s why you were denied. For the fall, you will be an independent student and YOU might qualify for an increased direct loan if the number of credits qualifies. You might also qualify for a Pell grant, but again only if you are taking enough credits. It sounds like you were offered the extra direct loan, which for a senior would be $7500 plus $5000, but only half for each semester, so $2500 extra. If you aren’t registered full time, it will be less.