What kill method is the vet wanting to use for your dog? There's 2 methods that I know of, the fast kill method, and the slow kill method. As far as I know it's the slow kill method that requires the dog to have limited exercise for 9 months or more, and it is not a recommended method, it also means monthly injections. The fast kill method means limited exercise for a total of 8 weeks, and there are 3 injections. I'm thinking that your vet is doing the fast kill method but I've no idea why he'd want you to keep your dog quiet for half a year. https://www.brewstervet.com/sites/si...eatment%20.pdf
Personally I'd ask the vet for a sedative to help keep my dog quiet, and would explore any crate games, training games, nose work, etc. that I could to try and keep him occupied. I'd also ask for another heartworm test be done to make sure that it was not a false positive that came up on the test.
There's a reason I'm saying get the treatment. I've seen more then one dog die of heartworms due to owners not having their dog on preventative, and waiting way to long to take the dog do the vet when the dog exhibited symptoms. It's not an easy death, the heart is literally clogged with worms, the blood is not getting oxygen, and the abdomen fills with fluid. I've also had to treat my rescue dog for heartworms, and know a few other people who have had to have dogs they adopted treated. My dog did fine with the treatment, and all but 1 of the other dogs also did well. The dog that didn't did survive treatment but got very sick from it.
The thing with heartworms is that the longer you wait to get the dog treated the harder the treatment is going to be, and if the dog does have heartworms he will eventually get very sick and die from it, so waiting is not going to get you anywhere. That's the other reason I say to just get him treated if he has heartworms, but double check to make sure the test is not a false positive, and make sure that the vet does a heartworm antigen test as it's the most accurate.