Did I commit a sin because of the problems that arose after objecting to the amount of the deferred dower (mahr) and the subsequent separation from my fiancée, to whom I am still attached, even though I later agreed to pay the amount?

You bear no sin for refusing an exorbitant deferred dowry or for breaking off the engagement because of it. However, sin and burden fall upon you due to your relationship with the girl before the legal marriage contract, if it involved anything forbidden, such as being alone together (khalwa) or similar acts. You both must repent and cease these actions until the legal marriage contract is concluded.

You can intercede with influential people to facilitate the dowry, as the deferred dowry is a debt upon you unless your wife waives it, which she should do.

If the matter is not facilitated or you find difficulty in it, then seek another woman of piety and good character.