I would hope that you were not told to take the stand to confess your guillt, which is what you are suggesting. That would be malpractice. Sometimes, however, the only way a defense will come out is if the defendant takes the stand on his own behalf. The good news is that he gets to tell his story during direct examination. The bad is that the prosecutor will try to trip up the defendant and tear his testimony apart if he can. If that's what happened to you, I'm sorry to hear it.
Yes after a jury trial you have 30 days to file your notice of appeal. From there you would need to have your lawyer turn the file over to a post-conviction attorney. Your lawyer couldn't do your appeal, because it would be a conflict if you are going to claim that you did not have the effective assistance of counsel. But he can file your notice and turn the file over to whoever will do your appeal.
It sounds like you also feel that the jury went against the weight of the evidence in convicting you. Please keep in mind that a higher court won't reevaluate the facts of the case. They leave that squarely with the trial court who had the benefit of seeing and hearing everything that happened. The court will look for mistakes of law and errors in the judge's ruling and also assess the fundamental fairness of your tria,.
If you don't know whare to go in order to find an appeals lawyer you can contact your local bar associations legal referral service. If you were elegible for a public defender, there are also appellate defenders. Your lawyer could get one assigned for you.
If you have gone beyond the 30 days to file your notice of appeal, you can be limited as to the grounds that you that you can assert for your appeal. About the only one that would be left to you would be having learned about some newly discovered evidence that were it known about before your trial, would have resulted in an acquittal
. I don't see that you have anything like that going for you. But you can see what an appeals lawyer thinks after he's seen the file.