F1 and H1 are being applied in parallel


I got admits in two universities for fall 2017 and my employer is applying for H1 this year.

I definitely need to apply for F1 visa as the classes start in August even before H1 comes in to force.

So, please suggest me, if applying both at the same time will be a problem and what can I do??

Nope, not an issue. You can apply for both simultaneously. But can only enter and remain in USA on one status.