I used to have dailies, switched from monthlies and, despite the increased cost, I much preferred them but I wouldn't have taken them out and put them back in, I would have put a fresh pair in and would have some extras about to do this.
That said, that would be rare as due to my eyesight I would wear them all day/evening until I took them out when I got home and wasn't going out again, and would only take them out otherwise if my eyes were sore or a problem with the lens. I cleaned and put it straight back in on occasion though.
I would ask one of the opticians though (rather than a receptionist) if they are ok to be kept in special solution for short periods, like a few hours.
You could also ask to trial other monthlies, depending on the issue. Did they say what exactly you are allergic to in the monthlies which is not in the dailies and whether there are other options.
I can't wear them any more as my eyes are too dry but I do miss them.