Salaam brother!

Thank you for putting your question to us and seeking our advice; you are most wellcome to it!

Brother let me just clarify this at this stage that I'm just a laymen who expresses his thoughts so please dont take what I say to be authoratative at all from an Islamic legal point of view and for a trustworthy Islamic position on anything, advice/guidance should be sought from qualified scholars

After reading about your situation and circumstances brother, basically what I think is this:

There is all the Islamic advice of how one should not disobey their parents etc, and have patience untill they find a girl for you; one with which their happy with, or untill one comes along with who'm their happy with too, but i am thinking here brother that this case may be best decided on the disposition of both you and your gf; will you both be able to keep away and heed the advice of your families?;

given what has allready happened, that after being parted you both couldn't stay away from one another, I think the answer is, probably not, therefore, in this situation the best action to take may be to protect yourselves from sin first and foremost, and that will mean to get married with or without your families/parents support/consent and there is a dispensation in Islam for marriage being valid even without parents [or a wali's [guardians] consent [but there may be a problem to this depending on which school of thought you both follow; if you are both Hanafi's [most people of the indian subcontinent are], then there is no problem, but there may be if you both adhere to any of the other 3 schools; there could be an allowance here of adherants of other schools skipping to the Hanafi opinion on this, due to the circumstances and/or a fiqh of minorities applying, but this should be clarified from a scholar]

If brother you think your family [and your gf thinks her family] will be so upset that their discontent wont heal, then it is really upto wether you both can constrain your feelings for one another and stay away and give precedence to your family relations more than the relations between you both [which will be the best option in this scenario], but if you both feel that this upsetting of your families will be only temporary and soon they will inshALlah accept it and be happy with you both, then I think taking measures to stop you both from sinning will be best and thus to go ahead and get married

hope this helps brother

Salam