You have not said what jurisdiction you are in, so it’s impossible to say with precision. Where I live in Florida, USA, there’s really only two places that something like that would show up: credit report and the "official records" of the county, which includes deeds, court judgments, etc.

To know if your situation would be likely to show up, first you have to know if there was actually an order from the court giving possession to your landlord. A copy of such an order would have been mailed to you at the same address where you were served summons for the eviction suit, ostensibly. If you never received such a document, either there was no final judgment of eviction or something is fishy. If there was no final judgment, that implies the case was either voluntarily dismissed by the landlord or abandoned and dismissed by the court after some period of time for "failure to prosecute" or "want of prosecution". All the circumstances leading up to your giving the lawyer money and ultimately leaving the property really don’t have anything to do with it … it’s all about the judgment, which is an order of the court.

What shows up in a credit report is actually, generally speaking, a list of judgments against you as recorded in the public records of your jurisdiction, so if it doesn’t exist as a judgment in the first place, it really can’t show up on your credit report. HOWEVER, if your landlord was a decent sized business entity, it might be possible that they reported your rental payment history as if the property was a line of credit and you were making payments on it. If so, that would be separate from the eviction judgment concept.
References :
Professional legal research 15+ years.

You might would want to seek the property management companies in Central Florida. They are the best at getting you into a rental, whether it be a condo, townhouse, apartment or house. Thy would be able to provide you a list of rental units, the requirements and applications to qualify and anything necessary to rent one of the units.

Each management company would have a separate rental list.

I hope this has been of some benefit to you, good luck.

"FIGHT ON"
References :

The callous greed of these benefactors is evidenced in their obdurate opposition to any contribution on their part to rebuilding our economy. We helped the wrong people.

We would have acted much more prudently had we bailed out most of the people who have lost their homes to foreclosure. The banks and other speculators holding questionable mortgages would have been paid off and thereby avoided bankruptcy without the hundreds of billions we poured directly into their coffers. Millions of homeowners would still have their homes; these houses would not be flooding the market depressing the value of residential estate.

With millions of people able to keep their homes and their equity, personal spending would not have fallen as precipitously as it did. Portfolios would not have lost their value; as a result, the big banks, insurance companies, etc., would have remained solvent and would have been able to keep all (or most of) their employees. With more people able to spend money, fewer businesses would have lost their customers. With more businesses solvent, fewer people would have lot their jobs.

The bailouts accomplished very little beyond quickly restoring to a few ultra-rich speculators and to monopolistic Corporate America the wealth (and much more) that they had lost in the early part of the recession. Now these corporations sit awash in $2 trillion, which they do not invest, their promises to do so notwithstanding.

We can still salvage our economy. Since the greedy elite will not invest this immense treasure without assurance of immediate profit, we should take much of that idle capital through taxation and spend it on rebuilding and modernizing our infrastructure. Doing so would not be MAKING work; it is doing work that is long overdue. In the process, we could put millions of Americans back to work–and back to spending and restarting our economy.
References :