Is homosexuallity a choice...and if not what causes this to make people feel this way?
Anyone who has sexual relations with another does so by choice. Otherwise we would be like animals that have sex just because the other gives off an odor saying she is ready to be mated. If we choose to have sexual relations with one who is not our spouse, it is a choice. If we choose to have sexual relations with one of the same sex as ourselves, it is still a choice. (This, of course, assumes that the Calvinists are wrong about everything being predetermined in our lives by God, with no free will for man.)
Notice that I specifically talk about engaging in the sex act itself. This is because the Bible doesn't talk about homosexuality as a lifestyle, but as an act. The concept of "being a homosexual" even before performing the act is relatively modern, and foreign to the scriptures. The word Paul uses for "homosexual" is a Greek word he may have invented that would directly be translated "one who goes to bed sexually with a man."
The second part of your question asks what makes people feel this way (or, as I would phrase it, act this way). What makes a person lie, or cheat, or murder? Ultimately, any sinful act we commit goes back to our willingness to submit to temptation. "But every man is tempted, when he is drawn away of his own lust, and enticed. Then when lust hath conceived, it bringeth forth sin: and sin, when it is finished, bringeth forth death." (James 1:14-15)
Paul says people delight in such acts because they are unwilling to glorify God. Because they refuse to worship Him, he allows them to act in ways that will lead to their destruction. "Because that, when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened. Professing themselves to be wise, they became fools, And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things. Wherefore God also gave them up to uncleanness through the lusts of their own hearts, to dishonour their own bodies between themselves: Who changed the truth of God into a lie, and worshipped and served the creature more than the Creator, who is blessed for ever. Amen. For this cause God gave them up unto vile affections: for even their women did change the natural use into that which is against nature: And likewise also the men, leaving the natural use of the woman, burned in their lust one toward another; men with men working that which is unseemly, and receiving in themselves that recompense of their error which was meet." (Rom 1:21-27)