Sorry to give you bad news but, unless your judgment debtor has non-exempt assets in Texas, it is very likely that your Texas judgment is pretty much useless.
"I won my small claims case today. I got a default judgement b/c the defendant no showed."
*** Okay, that simply means you got a default judgment. And since the defendant isn't in your state, your judgment is probably useless.
"Problem is, I still don't have the property I sued for, which is a diamond ring."
*** I don't really understand your excitement. Texas small claims courts can't order the return of property. They here only cases of monetary claims. Clearly, you either misunderstood the court or haven't read the judgment.
Texas Gov Code:
"§ 28.003. Jurisdiction
(a) The small claims court has concurrent jurisdiction with the justice court in actions by any person for the recovery of money in which the amount involved, exclusive of costs, does not exceed $5,000."
"The defendant is in CT."
*** Oh, oh!! Big problem. Your Texas judgment is useless in Connecticut and you will need to try to domesticate it there if you have any hope of trying to enforce it. And even more bad news, CT doesn't allow domestication of default judgments from other states.
"How do I go about getting my property back?"
*** Another problem. Connecticut small claims is a 'money only' court also. If you want to sue for recover of property, you have to use a higher court and that would likely require the services of an attorney.
"Do I have ANY recourse"
*** Probably not in Texas. Your only real recourse would be to file your lawsuit in HER home state (and where her assets are). If you get a judgment there, then you can use that states laws to attempt to enforce the judgment there.