and get a bad allergy to the different pollen there, would you become used to it over time if you were to live in that country?

I wouldn't think so. It would be just like moving somewhere new in the US and having a reaction to local flora.

I have never heard of anyone getting "used" to pollens anywhere. An allergist told me that inhaled allergens get worse with age.

When I was in Kosovo, I had the worst allergies of my entire life. They lasted the entire time I was there.

And when I was in Germany, they weren't that bad, truly seasonal (for a change), and they never changed in the four years I was there.

Just anecdotal evidence for a "no."