Are there any jobs in the military related to engineering physics?

there are jobs for anything and everything you could imagine, contact a recruiter and tell them what you want to do. Don't let them put you into something you wont want to do though, and be sure your going in for the right reasons. (free collage money isn't the right reason)

Yes the Army Corp. of Engineers and the Navy SeaBees.
Typically you will need to go to a contractor for that type of position. That is a little more technical than your standard military type position. You may have a military overseeing the project in a Program Mgmt. type position.
No, our military doesn't fly planes, shoot bullets or float ships. We poke people with pointy sticks.

Of course the real trick for a US soldier is keeping that pointy stick away from the rear. (The soldiers to the rear don't know how to use pointy sticks and their have been accidents.)
Real Life.
yes the services all have engineering positions usually dealing with construction. There is nuclear reactor operation and maintenance. Possibly demolition as in clearing damaged buildings.
I would suggest if you want a position of any importance or in research you first seek out some advanced education such as a Bachelors in that area of academics then enter into ROTC while in college to help better insure that you get into that field. Also speak with a recruiter but keep in mind the recruiters job when they have a shortage is to recruit you not to give you what you want but to get a bonus for filling shortage areas. It is a me me world unfortunately.