Most apartments are constructed with sheetrocks on each side of the wall, held there by nails in 2X4s. Outside walls will have fiberglass insulation; inside walls may not.
Years ago, I had the opportunity to shoot the walls in an old house, to learn about bullet penetration. Some of the walls were recent additions, built to segment larger rooms, and used sheetrock.

ANY .38 Special bullet I tried penetrated both layers of sheetrock. I did not have frangible or Glaser bullets to try. But I learned that even the 148 gr. lead wadcutter bullet -- the standard target load -- punched through both sheets of sheetrock.
The 158 gr. lead roundnose had no trouble penetrating both walls.
I also shot my own reloads of a 158 gr. lead semiwadcutter at about 850 feet per second. Punched through like a pencil through Jell-O.
Testing was done using a Ruger Security Six .357 Magnum with 6-inch barrel.
Yep, fired a few .357 loads too. No question -- never going to be stopped by a wall.
The .22 Long Rifle bullet from a 6-inch barrel penetrated both sheets.
I suspect that the .32 Auto and .380, especially with full metal jacketed bullets, would penetrate both sheets as well.
On the rare occasions when the bullet didn't emerge, I dug a peekhole with my knife and learned it had hit an upright 2X4.
But on those occasions when the bullet encountered only both layers of sheetrock, it penetrated them.
I wish I'd had a .25 Auto and other calibers for testing.
But what little testing I did showed me that even the lowly .22 Long Rifle bullet cannot be trusted to stop within a wall.

As for the Remington 158 gr. +P load: I wouldn't suggest it. This is a load purposely made more powerful than a regular load. Hence, it will certainly penetrate both layers of sheetrock easily.
You inquired about a bullet that wouldn't penetrate much; any +P load is not what you want if that's your requirement.

As to your problem: I'd suggest a Glaser bullet. If that's beyond your means, then load your .38 with 148 gr. wadcutters. It may penetrate the wall, but its flatnose will cause it to lose a lot of energy doing so. Consequently, it may not prove as dangerous if it does hit someone on the other side of the wall. At least, not as dangerous as a pointed bullet or one launched at greater velocity.

You may also wish to consider using a shotshell in that revolver, for your first shot. Anyone hit with it will experience excruciating pain. Aim for the body, not the face. If you aim for the face with a shotshell, the prosecutor and jury may hold it against you, especially if the aggressor is blinded.

When I lived in an apartment in Idaho, I created shotshells and multi-ball loads for my Marlin .45-70. Three .457 balls loaded in a case, and emerging at 1,000 fps, could ruin anyone's day.
Today, for home defense, I use my Walther PPK in .380 caliber. Or my Smith & Wesson .38 Special with 4" barrel, loaded with my own loads of a 158 gr. lead semi-wadcutter at about 850 fps.