Yes, Israel should be worried about attacks from neighboring Islamic countries. The threat of these attacks is always a possibility. However, with the unrest in the Middle East at this time, there is a higher risk that a military attack against Israel will take place. Thus, Israel and its allies should be prepared.
Israel is in a very fragile state. The country is in war, turmoil, with numerous other social, political, and economic issues. Any country is such a delicate state s is subject to attacks from near by countries especially if the surrounding countries are volatile much like the ones surrounding Israel are.
I have to admit that sometimes Israel does itself no favors. Benjamin Netanyahu is a leader that picks battles and picks sides where he doesn't belong. For example, in the U.S. Government. The behavior of the government's leadership makes Israel more vulnerable to attacks and a lack of cohesive effort to respond appropriately. Leadership change might help forge a more peaceful resolution. Hopefully, Israelis will get Bibi out sooner than later.
Israel should not ever be worried about any kind of military attacks from neighboring Islamic countries because Israel is way beyond capable at being able to take care of themselves and beating any enemy that has ever tried to attack or defeat them. The seven day war is one good example.