No, you do not have any proof from Scripture that it is another dimension. In fact, Scripture does not support your contention when it says the following:
Revelation 9:14 Saying to the sixth angel which had the trumpet, Loose
the four angels which are bound in the great river Euphrates.
Note that this verse explicitly says that four angels were bound in the great river Euphrates. The great river Euphrates is not in another dimension; it is on the earth.
Note also that what the text says signifies that there were only four angels bound there--not all the angels.
The following passages support that interpretation because they speak of the dragon and his angels fighting in heaven after what is spoken of in Revelation 9:14.
Revelation 12:7 And there was war in heaven: Michael and his angels fought against the dragon; and
the dragon fought and his angels,
Revelation 12:9 And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and
his angels were cast out with him.
You could try to say that "his angels" in Rev. 12:7 and 9 signifies only the four angels that were released in Rev. 9:14 but the text does not say that will be the case. You would have to prove that is what "his angels" means in Rev. 12:7 and 9.