Peace be unto you,
Dedic.
First, I am sorry to hear about your girlfriend's very difficult situation.
Second, they will not prescribe her T3 ever. T3 is almost never used. T4 is much more stable.
Third, T4 will only be given if she develops hypothyroid. Many patients will simply become euthyroid after the therapy, and therefore she might not require T4 at all. However, if she does, then she will be prescribed T4.
Fourth, it will only get better from here on out, God-Willing. She is on the road to recovery, and she will get better, God-Willing. God says:
"Verily, with hardship follows relief." (Quran, 94:5)
Fifth, with regards to why she was given this disease, know that Prophet Muhammad [s] said:
“By the One in Whose Hand is my soul (God Almighty), no believer is stricken with fatigue, exhaustion, worry, or grief, but God will forgive him for some of his sins thereby—even a thorn which pricks him.” (Musnad Ahmad)
God says in the Quran:
“Do men think that they will be left alone on saying, ‘We believe’, and that they will not be put to the test? And certainly We tested those before them, so that God will differentiate those who are true from those who are false.” (Quran 29:2-3)
"We shall certainly test you, until We know those of you who strive their utmost (for God) and who are the steadfast; and We shall test your reported mettle.” (Quran 47:31)
“Or do you expect to enter Paradise without facing such trials as did those before you?” (Quran 2:214)
“We will surely test you with something of fear and huger, and the loss of wealth and lives and the fruits (of your toil), but give glad tidings to those who patiently persevere, who say—when afflicted with calamity—'To God We belong, and to Him we shall return!' They are on those whom descend blessings from their Lord, and Mercy. Such are the rightly guided.” (Quran 2:155-157)
“You shall certainly be tried and tested in your possessions and in your lives; and you shall certainly hear much that will grieve you…But...patiently persevere and be pious!” (Quran 3:186)
“And none shall be granted such goodness, except those who are steadfast.” (Quran 41:35)
“And it may be that you dislike a thing which is good for you and that you like a thing which is bad for you. God knows and you do not know.” (Quran 2:216)
Prophet Muhammad [s] said:
"The greatest reward comes with the greatest trial. When God loves a people, He tests them. Whoever accepts this, wins His Pleasure.” (Al-Tirmidhi)
“Paradise is surrounded with difficulties (i.e. in this worldly life)…”
“Trials will continue to befall the believing man and woman—with regard to themselves, their children, and their wealth—until they meet God with no sin on them.” (Al-Tirmidhi)
“On the Day of Resurrection, people will wish that their skins had been cut with scissors in this world, when they see the reward of those who were struck with calamity (in this worldly life, and who were patient).” (Al-Tirmidhi)
“How wonderful is the affair of the believer, for his affairs are all good, and this applies to no one but the believer. If something good happens to him, he is thankful for it and that is good for him. If something bad happens to him, he bears it with patience and that is good for him.” (Sahih Muslim)
God says:
“We shower Our Mercy upon whomever We will, and We never fail to recompense the righteous. Additionally, the reward in the Hereafter is even better for those who believe and lead a righteous life.” (Quran 12:56-57)
God reassures His creation:
“By the Glorious Morning Light, and by the Night when it is still! The Guardian-Lord has not forsaken you nor does He hate you. And verily the Hereafter will be better for you than the present. And soon will your Guardian-Lord give you that wherewith you shall be well-pleased.” (Quran 93:1-5)
I'm not here to shove my religion down your throat, only to make you feel better. The quotes I have posted above are universal in application, and could apply to even a Christian or whatever religion you belong to, so long as you believe in God Almighty. Know that everything that happens is from the Wisdom of God, and the believers submit to His Will with patient perseverance.
Peace.