It should be noted, that 88 civic's have a different rear control arm design than the 89-91 civics. Thus most shocks for 4th gen civics mean that if you own a 88, you must go out and buy rear control arms outta a junkyard from a 89-91 hatchback, 4-door, or CRX (Si ones if you can find then gives you more rear swaybar choices). Unless you get the progress rear sway bar which works regardless if you pick up Si rear control arms or not. I use to have a 88, i'm warning you before you make the same mistake I did!
Also I'd recommend tryin to do possibly shocks, then maybe new urathane bushings, and springs if you can afford them still after that. I had just bushing and shocks on my 88 DX hatch for a long time and I handled damn well I still miss that little car. The noise is probaly either just old shocks or POSSIBLY a dead bushing you never know.
Side note: The control arms on a 88 DX resemble that closely of the intergra type-R....hmmm
If you ever get the rear control arms off your DX, keep one and crawl underneith the back of a Type-R with it and compare...you'll scare yourself lol.