OK, I'm assuming that you are allergic to ALL tree pollen here! (As other posters have said, maybe get this checked out, from what I understand some varieties are way more allergenic than others - but I am no expert on this and everyone is different too!).
There are two main kinds of trees. Some have both male and female flowers on the same plant (monoecious). Others have male and female flowers on different plants (dioecious). You want a female dioecious tree, as this will produce no or minimal levels of pollen.
A classic example of a female dioecious tree is a holly with berries. The confusingly named Golden King is actually a female holly busy with lovely variegated foliage and bright red winter berries. However, bear in mind that you'll only get loads of berries if there is a male holly bush close by (in another garden).
Some varieties of acer are dioecious too - I think some plants of Acer rubrum 'Autumn glory' are. (And it's like fire in the autumn!)
You say you are OK around apple, which is interesting - I suspect this is because apple has proper 'flowers' with male and female parts to them - the pollen in these tends to be heavier, as it is carried by insects rather than blown around in the wind. If I'm right, then you'll also be less allergic to other trees with beautiful, large flowers - like cherries, magnolias, crab apples.