@Tyler454 Is the downstairs neighbor another of the host's guests? If not, and it's just an apartment with a tenant, that isn't anything your host has control over. It's like blaming the host because there's traffic noise.
If it is one of your host's other guests, but the host doesn't have a no smoking policy, that's something you should have looked for in the house rules when you booked, not after the fact.
I'm sorry you're suffering, but when a guest has allergies or other special considerations, it's incumbent on them to make sure it won't pose a problem before they commit to a booking. If I was seriously bothered by cigarette smoke, I wouldn't book an apartment without first ascertaining whether it was a no smoking building or not.
If you can't open the windows and air the place out, about all you can do is decide whether to stay, or cancel the rest of the stay and leave.
Or go downstairs and talk to the tenant, explain politely that the cigarette smoke is really strong upstairs, that you are allergic, have two more days on your booking, and see if he would be amenable to smoking outside, or out the window, or at least not in a room where it comes up in your bathroom.
It's actually a big problem for a lot of hosts, even ones who have no smoking policies and very much do care. Because some guests will ignore that and smoke anyway, and the host has hours of work to try to get the smell out of everything before the next guest shows up.