Is the oath I uttered considered a solemn vow, and will I incur sin and be guilty of perjury if I violate it?

An oath is based on the intention and purpose of the swearer. If you leave the area from which you swore not to leave, for work purposes, then you have broken your oath and atonement is incumbent upon you. It is important to note that, in principle, atonement is not repeated for repeated breaking of the oath.