1997 528i doesn't shift between 1st and 2nd but if I shift to S3 and back to Drive it shifts

Do You do have reverse

Solenoids inside the transmission or the control module.

Tranny most likely shot. I believe yours is a T-5, I had the same issue years back but in 3rd gear. Usually the clutch going out is a gradual thing. So I would have a tranny shop look at it. Maybe find a cheap rebuilt tranny for ya.Look online or a trusted shop.

Well go get your car fixed by a mechanic or it something might be jammed inside

shift solenoid needs to be replaced or the speed sensor

Your problem could be the motor mounts. To check have your helper shift from drive to reverse with the engine at idle.

-----check possible tps [throttle position sensor ]circuit for damage or faulty sensor----if good check the fuses and trans harness for shorts damage or disconnection,check o2 sensors wiring possible ground to exhaust ,or internal leak 2nd gear apply circuit[servo assembly or 1-2 accumulator] or poor pump pressure

change fluid in trans add lucas for trannys let me know if theres metal in the pan or if you have trouble tell fixya bout me ok

Shift error codes are enabled not only if the solonoids are faulty, does your scanner show you the solonoids switching? you could have a wiring fault. It could also be the pcm not allowing the solonoids to activate. These complicated systems are very difficult to diagnose for us profesionals with all the scanners and machines we have. Find a transmission shop in your area with a system to drive the vehicle bypassing the computor system, this will determine electrical or internal trans failure. But before you do anything check your conections from the transmission to the pcm. Also all the engine conectors and earth straps.

Have you tried taking the car in for maintenance? Usually on most (older) auto transmissions there is a hose coming off of the exhaust manifold or carburetor area that provides the pressure for the transmission fluid. If that hose doesn't have a good seal, your shifting may be difficult and the transmission may not stay in the gear you want it to.