I have been stung many times by bumblebees and have also developed a reaction to them.
As others have said, the nests won't last much longer at all. A couple of weeks tops. The new queens have probably left by now. Could you wear thick clothes, hat, scarf over your face and goggles to collect hay for 10 days? Get someone else to get it out for you?
Don't breath anywhere near the nest - its the CO2 that sets them off.
When its that serious a reaction, I'd advise to play it safe and remove the nest. honey bee keepers are unlikely to remove it for you. Do not work alone. It needs to be done after dark, with lots of thick clothing, every bit of skin covered - wear gogles or something. Then its common sense, find the nest (I guess under a few bales?) and have a box ready to put the whole lot in. Without breaking it, scoop the whole thing into the box, ensuring its the same way up. Close box.
Use a dim light with a red filter to see what you're doing.
Put in new place (ideally >1Km away, but wherever you can), somewhere sheltered. Unplug the entrance hole (should have said there needs to be a hole) and leave them to it. A box with a terrocotta pot over the top is not bad. Needs to be wether resistant.
If the nest is burried under bales and inaccessible, and too dangerous for you to leave for two weeks, get pest control in to destroy it. Many say they won't kill a bbee nest, but if you explain the severity of the situation, someone ought to.
Hope this helps.