Okay, I am assuming that your Civic has the automatic transmission installed because your description. in some spots, can be read either way. And, with that said, what you are experiencing is a simple case of “limp home-itis.”
Although you haven’t given me much to go on as to a specific diagnosis, I can tell that if your Civic revs and shakes when going from second to third and sometimes revs like it is in neutral then it is trying to shift into limp-home so you get home.
Now, it could be that the reason for the limp-home indication is that the torque converter is shot, however, there are other problems that can cause your Civic to act similarly. For example, if the tranny fluid is sludgy and dirty, it may not be able to pass smoothly through some of the hoses and galleries through which it has to go. In that instance, your shifts will be delayed and slipping.
It’s also possible that the bands and clutches have had it. Since it is happening through the range of the transmission, I would suspect that you’ll have to have them swapped out for all of the gears. And, if that is the case, then you are looking at a rebuilt transmission which will cost about $3,600, given today’s repair guides.
It is also possible that your Civic’s valve body could contain one or more check valves that have become lazy due to deposit buildups and because the springs have also become lazy. In this instance, your transmission will act the way you describe it.
Finally, one more thing that I can think of that might cause your transmission to act the way it is acting is that the shift-control solenoids are either sticking or failing which could cause the tranny to act in the manner you describe.
At this stage of your car’s life, given its age, I think you are looking at a rebuilt transmission. I hope this helps. Let me know if you have any further questions.