If you have a three speed automatic, you have a 32RH, also known by various names like A904, etc. Automatic transmissions do not have sychros, so that is not your problem.
It seems to me that you have two things wrong, one, your low/reverse planetary is shredded, and, two, your clutch packs are fried. Whether or not either or both are true, you definitely have a major problem and should not drive your Jeep until you get it fixed.
Drop the pan. If you see chunks of metal in it, your planetary is toast. If the fluid smells burnt, your clutches are toast. If neither is the case, you might want to check your drive lines and rear end just in case, but I fail to see how they could be giving you those symptoms.
If your transmission is toast, it is time for you to learn how to fix it yourself as you probably cannot afford to have a transmission shop do the work for you. That transmission is easy to work on with nothing complicated about it at all. It would be a great starter project for you to learn about how transmissions work.