If you have a model number stamped steel frame gun, you can probably shoot any factory .38 special ammo that you choose from it. While the factory has told people different things at different times about firing +P, my personal choice has always been to go ahead and do so. If the gun breaks, or suffers for it, then I'll dispose of it. Carry guns are by their nature potentially disposable. If something is a rare and valued heirloom, then don't use it for a main line defensive weapon - the same as you probably wouldn't drive a minty early Corvette to and from to work each day in heavy traffic.
+P ammunition would be extraordinarily unlikely to cause a catastrophic failure in your gun. It *might* somewhat increase wear and tear, but so will carrying it or firing it at all.
Thus your problem becomes one of "What is available". If you can find the Speer 135 gr +P, that's a popular offering. Some people prefer the Remington version of the old FBI load which is a 158 gr +P LSWCHP. Note that the lead is often claimed to be softer than the Winchester version which is felt by many to increase the odds of expansion.
If you can't find, or can't afford, those offerings, then try the Rem-UMC 125 gr +P JHP as sold in 100 rd value packs at Walmart.
If you can't find any of that, then also look for Remington Golden Saber, various Federal HSTs, etc and try to find something that your gun likes and that you can find and afford.