My cat is very sick and based on the doctor’s opinion it will be very expensive if it continues like this. I don't mind paying, however, at what point Islamically does it become too much? Is it my obligation to give the best treatment and if he will live in pain Islamically is it more merciful to put him down? Or do I not have that right to make the decision to take a life? Is that considered assisted suicide? I don't want to go to Jahannam.
بِسْمِ اللهِ الرَّحْمنِ الرَّحِيْم
In the name of Allah, the Most Gracious, the Most Merciful
It is permissible to put an end to an animal’s life if one has the conviction that it shall not recover. If it's suffering is of such that there is no hope for a cure then it would be allowed for that animal to be put sleep. Imam ibn Abideen mentions it is permissible for a dog or cat to be slaughtered for the benefit if it is close to death. One should try and take some benefit of the animal if one was to have it put to sleep as this would not waste the animal.
Only Allah knows best
Written by Maulana Irfan Ali
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham
 Raddul Mukhtaar vol 6 page 474