The ten day period for filing a notice of appeal makes me think this was a federal case, as my understanding is that in state court in South Carolina you have 30 days to file a notice of intent to appeal, so I'll assume that you're in the feds, where the time for filing a notice of appeal in a criminal case is 10 days.
First, it is possible there was no notice of appeal filed yet because you have not been sentenced yet. The notice of appeal would go in after the sentencing and since you are not locked up, I gather you may still be awaiting sentencing, which would explain why there has not been a notice of appeal filed (yet).
Second, you should keep in mind that, if this was a plea, there may have been a written agreement that waived basically all of your plea rights, assuming it didn't reserve any issues for appeal like the sentence, a denied pretrial motion, etc.. If there was such a reservation made or if you made what is called a blind plea without a written agreement, then yes, it does sound like your attorney screwed up, assuming it is more than ten days since SENTENCING.
Even if this is true, assuming you can demonstrate that you wanted to appeal your case and clearly communicated that to your lawyer, you can, at worst, file a 2255 petition saying that your lawyer was ineffective for failing to file the notice of appeal when you wanted it done and you should be able to prevail and then get the opportunity to appeal again.
There are details missing from this discussion. Your best bet is to speak with an attorney whose practice focuses on appeals and post-conviction work and then proceed accordingly. You should not delay in doing this as there are a ton of time-sensitive deadlines involved in this process for you.
The deadline to file notice of appeal in General Sessions Court in South Carolina is 10 days. If you instructed your attorney to file the notice of appeal and she did not, you can file a post-conviction relief action (PCR) and ask for a belated appeal. Before you do this, consult with an attorney as to whether you have grounds for appeal or separate grounds for ineffective assistance of counsel (also PCR). If the judge made a mistake of law you have grounds for appeal, but that is rare in a guilty plea context.
Regardless of whether it is state or federal you have options. In federal file a 2255.
If it is state court file a Pcr on all issues but also cite to white v.state and in addition to other relief ask for a belated appeal.
If you have any questions please contact me.