When my sister travels, I know that she can't travel without a mahram. But if I act as a mahram for her so she can travel, I am sexually attracted to her and the temptation is very high when we are alone together. I know that it's forbidden to have sex with her and I pray that I don't sin like that, but it is very hard in that situation with travel. Is it haram for me to be mahram for her because of this? How can I refuse to be mahram for her when she needs me to, when I can't explain the real reason without destroying the family?
Mahram is two-fold in Islam, one kind is the kind a person is Mahram with his wife or her husband, and one kind is the kind a person is Mahram with his/her parents, brothers and sisters from the same father or mother, Reza'ee brothers and sisters, uncles, aunts, grand parents, parents in law, and etc.
The former kind is the kind in which any (common) sexual relationship is allowed, while the latter kind is only to make the everyday life possible, no lust stimulation is ever allowed in this kind of being Mahram. Every person can look at his mother/sister/aunt/... face/hair/body-with-only-two-exceptions, can talk with them not necessarily seriously, and etc., but only if there is not lust stimulation, otherwise even looking at his sister's face may be forbidden.
If you cannot travel with your sister without lust being stimulated then traveling with her would be forbidden for you. If you are to obey Allah be sure that he will help you, just go one step for Allah for Him to come to you hundreds of steps. Also as much as I know (according to many Shia scolars, but not all of them perhaps) marriage is also obligatory for you.
No people are born the same way. Allah gives different tests to different people.
Most of the Islamic rules and regulations which are not clearly written out in the Quran or hadith were designed for the majority.
You could well be in the outlier of 0.01% (which is still 1000 in a million) which the average doesn't apply to. We can reasonably assume that most people do not have any attraction to immediate family members or do not feel sexual attraction towards the same sex. In a similar manner, eating human meat is not explicitly forbidden, because the vast majority of people don't have any natural inclination or outlet to do so.
But people are born with glitches of their own. Just because it's consensus, it shouldn't conflict with common sense.
And do not approach unlawful sexual intercourse. Indeed, it is ever an immorality and is evil as a way. (al-Isra' 17:32)
The ruling is clear. If by being with such a person, you are approaching unlawful sexual intercourse, it is forbidden. There are a lot of attempts to classify what "approaching zina" means, from veils to skin contact, but I believe this is all highly subjective and personal. No sheikh can cover the urges for all people.
I'm not sure what valid excuse can be given to tell your family that you can't be her mahram. A Freudian psychiatrist will tell you it's perfectly normal, so psychiatry may not be a great idea.
I do not really know what should be said about this except what Islam says in conjunction with basic common sense. In this case it would be best to stay away from her and I would also recommend that you get married as user owari has recommended. Secondly, seek protection from Allah for the lustful thoughts that you have. Avoid looking at anything that excites lust and most importantly, find the company of genuine Islamic scholars whom you can sit with and get Islamic knowledge. Indeed, knowledge makes one fearful of Allah. Another recommendation is that you try to make your prayers perfect and not rush through them. As Allah has said:
Indeed, prayer prohibits immorality and wrongdoing, and the remembrance of Allah is greater. And Allah knows that which you do. [http://quran.com/29/45]
Try it, pray like the Prophet (SAWS) said, that is, as if you are seeing Allah and if you cannot manage that at least be aware of the fact that He is watching you. (Phrasing of the hadith is mine.) While I do not claim to have the best of characters (far from it), I can say that I have seen this work with amazing results. Nothing can beat excellence in salaah for character-building!
You're talking about your own sister here!! You strongly sound like you have a very strong urge to commit insect -- the worst thing a human being (let alone a Muslim human being) could commit against a family member!
I think the best answer is given by David Wallace and i would like to second him: Go see a psychiatrist to receive professional help immediately! But in the meantime; stay away from your sister as far away as possible! You must firmly reject to be her "mahram" and must get out of the house if you're living in the same house and move to a different neighborhood --much better if you could move to a different city! The farther you could get away from your sister; the better it is for both your sister and you, as that way you're less likely to see her or run into her, hence gradually and eventually getting, Inshallah, rid of your terrible urges harming both her and yourself. And you really must cease to see and speak (even by phone) to your sister until you have completely --Inshallah-- stop feeling any sexual feelings toward her. And stay away as long it takes -- even if it means 1 year or 10 years! And i think it's much better if you do not tell her (or to anybody else, except to a psychiatrist) as to why you're avoiding or staying away from your sister. If you have -- even a tiny bit-- humanness and belief in Islam in you; then i strongly believe that you would do everything possible (as described above) in order to get very far away from your sister so as to avoid committing insect -- a revolting sin and crime in betraying not only its victim but also yourself as a human being and Muslim! And i believe you have enough humanness and belief in Islam to take the above-stated measures in order to overcome committing this soul-robbing sin and crime. Otherwise i don't think you would have come here on this forum to seek help.