This question has two elements, one specific to Even HaEzer (laws related to marriage) and another that is a classic Choshen Mishpat (monetary law) discussion.
The mishna[1] states that certain sivlonot (presents that a chatan gives to a kalla before their marriage) return to the chatan if they do not get married. There is a basic distinction between gifts in this regard. Since presents (including foodstuffs) that were meant to be consumed during the pre-wedding celebration were appropriate to be given even if the end goal of marriage was not met, they do not need to be returned. However, presents that were meant to last into the marriage are deemed to have been given on the condition of marriage and must be returned if the couple does not get married.[2] Although we usually say that conditions that can undo a transaction must be verbalized, when it is clear that a present is based on a future expectation, it is deemed conditional. This is true even if the kalla is not at fault at all, including if one of the parties dies.[3] Similarly, a chatan is required to return the presents that he received from the kalla’s side.[4] Thus, in regard to one element of the question, you are required to return the jewelry.
However, regarding a different relevant element of the question, your claims are likely to have merit. You spent a lot of nonrefundable money on wedding preparations, which now, by his backing out, is a loss to you. It is likely somewhat complicated to figure out how much of this amount the other side owes you, and it may depend on specific elements of agreements and on the chain of events that we are unaware of. We cannot and will not express an opinion without hearing both sides, and it might require a formal beit din setting to determine an exact solution. However, since the other side has resisted dealing with the matter, the question is about taking the law into your own hands by withholding the jewelry.
Taking things of value in lieu of payment that one believes he deserves is known as tefisa, and its laws are very complicated. Three of its biggest limitations are against unilaterally taking something as collateral for a loan, which the Torah forbids,[5] causing damage during the tefisa, and taking something when he cannot prove that he deserves it.[6] However, the main problem relates to the act of taking. If the other party voluntarily gave the object (as in this case), one can hold on to it as a guarantee until his rights have been properly addressed (whether by agreement, mediation, or arbitration).[7] While it is problematic to obtain the object through deception,[8] that is certainly not the case here.
Legal tefisa can also bring advantage when it is unclear to a beit din which side is correct. The plaintiff who is holding an object and is seeking payment is no longer the only one trying to extract something and upon whom the burden of proof lies. After tefisa, the defendant is seeking the seized object returned, and in some cases he will have a greater burden of proof than had their not been tefisa. (The details are too complex to discuss seriously in this context.[9])
All of this said, it is extremely important from a personal, spiritual, and practical perspective that the painful matter of a broken engagement be settled in as smooth a manner as possible. Extended recriminations and posturing can cause all sorts of problems for the futures of the former chatan and kalla. Therefore, one should make certain sacrifices to do what is smart, not just what is right or legally valid.