Ceiling fan turns in with recessed lights switch

[masonlafoon@ya]

I've installed some recessed lights in my den, where previously there was just a fan with a light fixture running off a single switch.

Now there are 4 switches; 2 for the recessed lights and 2 for the fan, at different entrances to the room. But I can't seem to get them running independently, the fan's fees wire will run hot with the lights' switch. I have traced all the wires to definitively label which wire is which, and seem to have isolated the fan's wires. But even if I leave them undone and just wire the 3-way switches for the lights the fan wire runs hot.... I seem to have reached the limit of my very limited electrical knowledge, and am about ready to call a professional. But if there is any hope for me to do it myself I would like to

Thanks!