Many employers just check convictions and since your case was dismissed, it won't show up on your criminal history check. However, some employers do check arrest records and that is a problem for you. A fraud or theft felony arrest is a huge red flag for an employer, a landlord, or potential creditors. They absolutely have the right to fire or refuse to hire you (or not rent to you or give you a loan) on the basis of this arrest, so you want to get this expunged as soon as possible.
Depending on the basis of the dismissal, you may either be eligible to expunge all of the records now or you may have to wait until the statute of limitations has run on the charge. Talk to a local criminal defense lawyer to get more specific advice.
I would absolutely seek an expungement of your charge. Many times employers will run back ground checks and see you were arrested. If they see something dealing with fraud the chances are you won't even make it in the door for an interview. There is a statute of limitations on felony expungements but if the case was dismissed because you did not do it then you do not have to wait the statute of limitations for the expungement. I would contact a criminal defense lawyer as soon as possible to get the process started.
I have found that most employers who run criminal histories have their investigator, employee, or whoever does the actual work, report all arrests regardless of the outcome. You will see the same few people at the courthouse all the time running new arrests for ambulance chasing lawyers, and running criminal records for others.
You should hire a lawyer to expunge your case rather than attempt to do it yourself because quite a number of people keep records including DPS & others, and you need to make certain that all are notified to clear your record for your efforts to be worthy. (You will have to pay a filing fee as well as the lawyer's fee.) I would not try to attempt to do this on your own. (Moreover, I have found that the petition sits around on various desks and lawyers who do them at least somewhat regularly know who to call & figure out where it is & what is going on. Unfortunately, you will not have the information necessary.)
If your case was actually Dismissed, regardless of why, the Dismissal should be reflected in your record. Ordinarily, you don't have to go back to Court to expunge the record. However, just to be safe, you may wish to visit the Court Clerk's office and ask them how your record reads. If it shows an Indictment, but not a Dismissal, then you may need to get an attorney to clear the charge from your record. If it shows its been Dismissed, then you more than likely don't.