Moving with bed bugs?

My husband and I have lived in this apartment for about a year and started finding bites on our skin after our neighbor moved in. We had the landlord call someone to inspect our apartment and couldn’t find anything. The inspector then asked to see the neighbors unit and long behold, they were literally covered over the walls. They were crawling under the carpet to access our apartment. The exterminator has been here about 4 times now and my neighbor still has the problem. I put duct tape all around the wall and carpet so they cannot enter. We were sleeping on the floor surrounded by duct tape and caught two bugs. After the last extermination I only found one bug alive and have not found any more on the tape. We want to get the hell out of here and have the concern of bringing them with us. We are going to stay at my parents, double bag clothing and blankets to wash them, and put our stuff in a storage unit until we can find a new place. The exterminator can’t come back again until the time we need to be out of apartment, we gave our notice. My question is if I vacuum everything, put it loosely in a box, and spray the bed bug spray all over some furniture, does it really work? Then leave the bigger furniture here and after exterminator comes, put it with the rest in storage and let off a fogger? We already had to throw away couch and not looking to throw out any more items unless absolutely necessary. Could this help solve our bed bug fiasco? Has anyone else been through this situation? Thanks in advance!!!