"Tire's Ain't Perttee" to quote an old snake oil salesman from early seventies sales pitch from TV. They are what is printed on the side wall. If you are curious what those numbers translate into English units that 'Am-ari-kans' understand, you need only look at this chart.
A narrow tire can be short or tall. VW bugs had a 145R-15 tire that was nearly thirty inches tall, to reduce rolling resistance and make for better mileage. They where closer to a motorcycle tire than a car tire. So the sectional width is not all defining. In the first link you will see three different tires with three different heights that have the same or very close sectional width ratio number (the ratio aspect is the 78, 70, 60, 50, 45, or 35 number on the tire that tells you width to height ratio).
You were asking about shocks before. Shocks will not keep a car body from hitting the tire. Worn out implies that there is little damping so the car is constantly oscilating (going to get you sea sick after a while). A new shock won't bounce up and down more than twice, but it won't hold the car up. That is the job of the springs.
I mentioned that your springs might not be original. This is because the base model car had mono-leaf springs that would wind up and cause wheel hop. They were frequently replaced by J.C. Whittney's three leaf replacement springs. The factory high performance cars had four (for a SBC) to five (for a BBC car) to six rear leaf springs (for TransAm racing) depending upon the application. So if you still have a Spicer ten bolt (as opposed to the AAW corporate ten bolt), but have mult-leaf springs they could have been replaced in the past.
Don't know what you have for suspension; but it makes a difference in how the car handles and performs from grocery getting cruiser to race car.
I wrote more on the subject in this Sticky under Suspension: