Some of us, without much or any experience, have tried DIY repairs and been blessed with beginner's luck. On other occassions we have spent a lot of time and likely money making a short-lived repair. You have received differing advice from others, none of whom have actually seen the wound or even a picture of it. My suggestion is to let a pro repairman look at it and offer his advice. (A salesman is likely to try to sell a new tire.). My experience, upon which I base the suggestion is as follows:
Shortly after buying my tractor I ordered a snowblower. As I did not then have forks, I borrowed my neighbor's 1966 JD 300, pallet-fork-equipped, industrial tractor with gear drive and iffy brakes. I managed to get the blower out of the delivering semi-trailer and into my driveway without incident, but during later maneuvering I put a fork blade through the sidewall of a rear tire of my own tractor. A little good fortune was that a local tire company had their commercial/industrial shop about 5 miles away. The help there was perhaps amused but definitely sympathetic when I showed up with a virtually new (spew vents or "hairs" all over the treads) tire with a slit in the sidewall. A new tire would have cost several hundred dollars; I was happy to pay them $165 for the repair. That was over 8 years ago, and the tire has given me no problems.