The RPMs shoot up to between 3000 and 4000, but there's no acceleration. When this happens, the brakes get harder to press.
The symptoms you describe for your Oldsmobile Alero lead me to believe you may have a vacuum leak. It is very possible that one of your vacuum lines is starting to fail and this can duplicate a transmission slipping out of gear. It will also produce the experience of a hard brake pedal, as the brakes require engine vacuum to assist you in braking. To be 100% certain, it may be time to enlist the assistance of a certified mechanic to come by and inspect your Alero with you. With use of a scanner and a vacuum gauge, they can monitor the engine vacuum as well as the transmission during acceleration. They will be able to identify if this is indeed the problem or if these symptoms are a result of another problem. Once the cause of your symptoms is identified, they will be able to make the repairs necessary so your Oldsmobile can be driven without worry.