What you have to do is "reopen" your claim. You get into the system and Tell the person you talk to about what will happen. It won't be any more difficult than the initial move was. Okay, we assume you filed a claim for benefits. You had monetary eligibility to draw some amount a week for so many weeks. We assume that since you have not received anything saying the claim was approved that you were still in the adjudication process. I believe this was the post where everyone turned themselves wrongside out about whether or not you could continue to work at your self employment job, and I assume that the FL system told you it was fine to do so. I am assuming you haven't heard yet whether the claim is approved or denied. Is this correct?
We also assume that you began filling out certifications (doing certifications by telephone or internet) for each week that passed after you filed the claim, right? Okay, that means that if/when the original claim is approved, you'll have filed for and served at least two weeks, one of which you'll be paid for (the first week in the FL claim is a waiting week, you don't get paid for it.)
We also assume you did not file for the week you went to work, or that you filed and reported your gross wages made Sunday through Saturday for that first week. And that the next week, a full week of work, you did not file? Right? Now all you need to do is call in and talk to someone, tell them what has happened, say you want to re-open your claim. Do this on the phone, even if it's much harder to get in to speak to someone. If you try to do it totally on the internet, where you can't tell someone what has happened immediately, it will prolong and complicate the process.
Explain clearly that you showed up for work every day, that you did the job to the best of your ability, that you did not quit the new job. You were told by them, after a certain period, that you just weren't working out. Of course you will need to tell the exact truth, because whatever you say will be verified by the system through the employer, so if you did quit, you'll have to tell the truth and admit you quit. But if the idea of you not working there any more wasn't yours and they told you they were letting you go, then that should make it very easy for you to get back onto unemployment benefits.
If a person accepts a new job, goes to work, shows up every day and does his best, and the employer still doesn't like his work, and decides to let him go, he'll probably be approved for benefits. In cases of firing, the burden of proof that they had a good misconduct reason to fire the person is on the employer. Performance issues that are not misconduct based (such as being too slow, not having the necessary skills, making too many mistakes) will not disqualify you. Deliberately messing up, sleeping when you should be working, violating company rules about smoke breaks or texting on the job, stealing, absenteeism, tardiness, all the basic misconduct things will still keep you from receiving unemployment benefits, but basic performance, just not being good enough or fast enough, those aren't disqualifiers because they look at it as things the employee could not really control.
If you just quit because you didn't like the work situation, or the people you were working with, or didn't feel like it was paying enough, the burden of proof that you had a good work related reason to quit is on you, and it must be quite high, a VERY big reason to quit. Like being asked to do something dangerous or not being paid timely. So it will be much harder and much less likely you'll be able to pick back up on unemployment.
Either way, once you accepted the new job, and began working there, it became your last job of record. The decision to grant benefits will be based on this job, and even if your prior claim was approved, there is a chance this one won't be, and if so, there will be no benefits except the week or two you got before you began the new job. If the original claim happened to be denied, they'd look at first whether or not you'd made enough on the new job to have re-earnings, and then still consider the reason why you left or were terminated from the new job as to whether or not you get approved this time.