Well, you have a dilemma here. By using lightweight bullets you create a few different issues. First of all a light bullet will hit low all other things being equal. The lighter the bullet, the lower it will hit. Your Chief's Special was regulated for 158 grain bullets and that should be POA=POI.
The second issue is that a 90 grain bullet from a 2" barrel is going to be pretty anemic. Not a good SD rounds at all and lousy for POA/POI accuracy.
Shooting standard velocity 158 grain bullets or even better, 148 grain wad cutters (for practice) is fairly easy on the wrists. For self defense, I'd still step up to a 158 grain +P or at the minimum, a 135 grain GDHP. Yea, they will be more hurtful to shoot but in the case of a SD shooting that wil be the least of your problems.
If you just can't deal with the Chief's Special recoil, you could try a different style handgun such as a 9mm. Semi Auto's have a heavy recoil spring and slide that absorbs a lot of felt recoil! They tend to be much easier to shoot with less felt recoil and todays 9's are smaller, lighter, less bulky, while holding more than twice the capacity of your Chief's Special. So you would have way less pain, probably shoot better and would practice more. BTW, 9mm ammo is way less costly than 38 special and today's modern 9's (like the Federal HST or Speer Gold Dot) are better performers than the old 38 special.
Just something else to consider......