there are no personal relationships condoned by Islam between non-mahram* men and women. this even includes any unneccesary talking between the sexes, such that any conversation that does occur should be Tottally neccessary, and be busniness-like and formal. not flirtatious, and half-coy.
this principle, is based upon Quranic instruction, which tells us in surah Nisa "la taqrabuz'zinna" :do not go NEAR Zina (adultery/fornication). it doesnt simply tell us to refrain from commiting zinna like the commandments revealed to moses, it doesnt say "thou shalt not" but "dont even go near zinna"...from this, the accepted wisdom is that any events that Lead one to zinna are ALSO haraam, including having relationships as girlfriend/boyfriend, flirting etc etc you know what i mean.
with regards to the fact that the girl in this situation is a shia, i would say, and others may strongly disagree with me here, notably shia's i expect, that shi'ite articles of fatih directly contradict mainstream islam, which not even shias can deny is fundamentally sunni. there is no compatiiblity between shia beleifs, and sunni ones. and although this may sound fundamentalist-extremsist, i dont particularly accept shia's as people who subscribe to Islam proper. and sure i am fundamentalist, in that i value the fundamental principles of islam, and am not willing to be reduced an a blubbering apologetic sell-out or start dumbing-down islam to be more pallatable to an apparently politically-correct collective psyche.
so the muslim action-plan-list will look something like this:
1. cease all unnecesary contact with the shia girl, and any non mahram girl for that matter.
2. ask permission from youre parents to start looking for a wife. and remember, money and other pragmatic considerations are no argument for delaying marriage in islam, there are strong hadith to the nearest effect saying "he who marries in order to protect his chastity, Allah will make his sustenance easy (or) Allah will provide for him". (i think its in bhukari)
3. if you dont get married, fast. im sure youve heard this many times before, and know what im implying.
4. and if you insist on pursuing the relationship, against all islamic principles of modesty and chastity, incurring Allah's curse as a result, then atleast revert the shia girl to sunni beleifs. to do this, you'll need heavy doses of hikmah (use of a carefully considered approach) and bucketfulls of sabr (patience, in the face of adversity). its an uphill struggle.
5. and finally, find a decent scholar, or someone who is learned to some degree, to find out what you stand for as a muslim, ethically. its an obligation on all muslims to seek knowledge, especially knowledge pertaining to deen.
im hope i havent confused anyone (too much),
*mahram= person to whom marriage is, not only unthinkable, but not permissible, these include (for a girl)... (so obviously the parrallel opposites for a guy): her father, brother, maternal/paternal Blood uncle, grandfather, direct first nephews, and sons. there may be more, allah forgive me if ive left any out. other than the above people, all men are non-mahram to the hypothetical muslimah in question. lol, hope thats clear, inshallah.