Should she continue studying medicine or get married and study?

Firstly: 

The basic principle is that it is mustahabb to hasten to get married for the one who is able for that, because the Prophet (peace and blessings of Allaah be upon him) said: “O young men, whoever among you can afford it, let him get married, for it helps him to lower his gaze and protect his chastity. And whoever cannot do that, let him fast, for it will be a protection for him.”. Narrated by al-Bukhaari (5065) and Muslim (1400). 

This is especially important in these times when temptations are widespread. 

Moreover, as you have just started studying, this means that this waiting period will be very long, and this is not in the interests of young men or young women in general, and it is not in the interests of the engaged couple in particular. Whoever is able to get married at the age of twenty, there is no benefit in delaying it until he is twenty five, and so on. Moreover, having a lengthy engagement is not something good, because the couple will be in a state of suspension, as it were, even if we assume that there are no haraam things involved such as mixing or being alone together, etc. 

It should be noted that the one who fears that he may fall into haraam is obliged to get married, and it takes precedence over studying in the case of a conflict. No differentiation is made between men and women in that regard, if they can afford it. 

Secondly: 

There is nothing wrong with completing one’s studies after marriage, but is it possible to combine studies and household duties? This varies from one person to another, according to their abilities and circumstances. It also varies according to the type of study, and whether there are children or not. It seems that there are some people who can do it and some who cannot. 

We advise you to pray istikhaarah and consult people before taking this decision, and we ask Allaah to guide you to all that is good. 

And Allaah knows best.