Do i qualify for unemployment? should i apply?

Yes, from you description you would qualify for unemployment benefits because you have plenty of wage credits and you are losing your job through no fault of your own. You need to go to your local employment office and apply, they have all the forms you need. Don't bother with a letter from your employers HR dept., the company has to report employee earnings to the state quarterly so they will know when and where you worked. You will have to demonstrate that you are looking for work, in some states you can report online or on the phone. You can continue to draw benefits even if you move to Boston to look for work, go to the Employment office there and file an Interstate claim. Good Luck.