This is a shighaar (quid pro quo) marriage and is not permissible
Question

I am a young man and I did the marriage contract with my cousin (the daughter of my maternal aunt), but I do not love her, I love her sister. But I was forced into that because her brother would not marry my sister unless I married the one whom I do not love. The girl knows that I cannot stand her, but her family insisted that she marry me. Now I do not know what I should do.
Praise be to Allah.Allah has honoured man with reason and He has given him free will to choose that to which his religion, reason and character make him inclined, so that he may rise above the promptings of whims and desires and of the shaytaan. So the one who has been honoured in this way should not be heedless and respond to the desires of those who are around him and their hateful customs.  
In the Sunnah there is a prohibition on the kind of marriage that you have entered into, which is called nikaah al-shighaar (quid pro quo marriage). 
It was narrated from Ibn ‘Umar (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) forbade shighaar. Narrated by al-Bukhaari (5112) and Muslim (1415). 
A shighaar (quid pro quo) marriage is when it is stipulated that each man will marry the daughter, sister or ward of the other, whether there is any mahr or not. 
It says in al-Mudawwanah (2/98): 
What do you think if someone says “Marry your daughter to me for one hundred dinars on the basis that I will marry my daughter to you for one hundred dinars”? Malik disliked that and regarded it as a kind of shighaar. 
This is also indicated by the report narrated by Abu Dawood (2075) and others from ‘Abd al-Rahmaan ibn Hormuz, that al-‘Abbas ibn ‘Abd-Allah ibn ‘Abbas gave his daughter in marriage to ‘Abd al-Rahmaan ibn al-Hakam, and ‘Abd al-Rahmaan gave his daughter in marriage to him, that being the mahr of each (i.e., there was no other mahr other than each marrying his daughter in exchange for the other). Mu’aawiyah ibn Abi Sufyaan wrote to Marwaan ibn al-Hakam telling him to separate them, and he said in his letter: This is shighaar which was forbidden by the Messenger of Allah (peace and blessings of Allah be upon him). 
Some of the scholars regarded shighaar as an invalid marriage which cannot be gone ahead with. 
It says in Fatawa al-Lajnah al-Daa’imah (18/427): 
If a man gives his ward in marriage to a man on the basis that the other will give his ward to him in marriage, this is the shighaar marriage which was forbidden by the Prophet (peace and blessings of Allah be upon him). This is what some people call an “exchange” marriage, and it is an invalid marriage, whether a dowry is given or not, and whether there is mutual consent or not. 
But if one man proposes marriage to the ward of another man, and the other proposes marriage to the ward of the first, without any stipulation, and the marriages are done with the consent of both women and all the other conditions of marriage are met, then there is no dispute concerning that, and in that case it is not a shighaar marriage. End quote. 
See also the answer to question no. 11515. 
Thus it is clear that you have done something that is forbidden in Islam as well as being reprehensible in social and psychological terms. 
That is because marriage should start with consent and be entered into by choice. Islam is keen to ensure the consent of both parties, to such an extent that the Prophet (peace and blessings of Allah be upon him) said: “A virgin should not be married off until her permission has been sought.” Narrated by al-Bukhaari (5136) and Muslim (1419). 
If marriage is not done with consent then it is usually doomed to failure, so how about if the husband dislikes his wife as is the case here? 
Even more serious than this is the fact that you love the sister of the one with whom you have done the marriage contract. Your dislike of the one with whom you did the marriage contract and your love for her sister means that your nafs (self) will call you to consider haraam things, and the shaytaan will find a great opportunity to make sin appealing to you. It will also deprive you of happiness in your marriage and contentment and love between you and your wife. 
The reason for that is going against the laws of Allah and entering into a shighaar marriage. 
Our advice to you is not to go ahead with this marriage and not to respond to any attempt to make excuses. You should explain to your sister’s husband that connecting one marriage contract to the other is haraam, and renders both contracts invalid. He should keep his wife, but at the same time he should do the marriage contract again, because the contract is invalid due to the shighaar. If he refuses and insists on leaving her, then Allah says (interpretation of the meaning): 
“But if they separate (by divorce), Allah will provide abundance for everyone of them from His Bounty. And Allah is Ever All‑Sufficient for His creatures’ needs, All‑Wise”
[al-Nisa’ 4:130]
I remind you to fear Allah and urge you not to transgress His sacred limits by trying to get in touch with that girl whom you love. If you cannot marry her in a proper manner, then you have to cut off all ties with her completely. 
We ask Allah to guide you. 
And Allah knows best.