I am a Shia and the girl which I love is also a shia. She also loves me. We only talk to each other and have no sexual talk or act between us. Also we don't do other haram acts. And mutah is difficult for her and our family will not allow us to do nikkah at this age. So is it good to continue this or what should we have to do ?

Alhamdolillah good you follow the Sharia but it’s clear that none of the Islamic laws can authoriz you or any man or woman that they can have any close relationship (while they touch each other) other than a formal relationship e.g two employees working in same office or two students in a same school or college. So this excuse has no value that your parents are not agreeing so you can’t do neither temporary marriage nor permanent therefore you can have relationship because you both are na mahram for each other. Therefore the best solution in your case is that you can assure her that you want to marry her and when conditions will be favorable for you, you will propose her officially. Till then you should avoid to having such relation which could bring down yours and hers dignity in the society. Otherwise there will be many issues if you are neither office colleague nor class mates then on what basis you talk and meet each other? When Islam says that a young woman should not say salam to a na mahram man then how I can tell you that you can continue your relationship even if it has no bad intention