You should ok if you apply this week or next.
According to data from USCIS, there are 5000 left on July 6, and 4000 left on July 11. So you can assume H1B cap decrease 800 - 1000 per week.
If that is the case, cap will run out till Aug 8 or Aug 15.
Premium processing takes 15 calender days.
Also assume you use 1 week for paper work and mailing, we need 22 days to get a result from USCIS.
So if you file this week or next, you can know your result by Aug 8 or 15.
If you only count the time during which you need to get your files in, you probably still have 3 weeks buffer time.