A friend of mine has an older Elantra which is basically perfect and with more miles than yours. Your car was either mistreated or not maintained well by its previous owner. Elantras, if properly cared for, will go 200,000 miles or more before engine or transmission fails.
The “garage man” is shooting from the hip which is typical of those who are either ignorant or too lazy to find out the current facts. His “opinion” was true of earlier Hyundais, such as the Pony form the mid 80s. He’s about 20 out of date.
Please take your car to a reputable INDEPENDENT transmission shop (not a Chain like AAMCO) to get a full report. If it is “shot” it will be worth fixing if the rest of the car is OK.
Good Luck1