First, make sure your campaign is actually using XP penalties. Very few campaigns do.
Second, if yes, try to convince your DM not to—they are an awful rule that absolutely fail to achieve their goal, which wasn’t a good goal in the first place. They just end up making the game more difficult to run because it’s extremely hard to balance encounters for parties at different levels. A level is a massive thing in this game.
Third, you could ask to retcon your character to use cleric instead of healer: cleric is better in every conceivable way, including at healing, and this would solve your problem as well. Healer is one of the weakest magical classes in the game (second only to the adept NPC class).
Fourth, remember that devotion feats allow you to retake them to get more uses of them. This may very well be more efficient than some of the suggestions below.
There is only one feat that offers turn undead, and it isn’t good:
From Dragon vol. 305, and requires God-Touched from the same issue, grants a single daily use of turn undead. Yes, this is the option mentioned in the linked question: 3e material is 3.5e-legal if it hasn’t been explicitly updated or replaced, and God-Touched and Divine Channeler were not. Just re-taking Good Devotion is vastly superior unless you go the route suggested in the other question and use Extra Turning on top of this: God-Touched, Divine Channeler, and Extra Turning results in 4 uses of turn undead, better than the three uses of Good Devotion you could get for re-taking that feat that many times, and you could continue to take Extra Turning from there. If you can get these feats as items, per Arms & Equipment Guide (which also hasn’t been updated for 3.5e, and so could be legal in a 3.5e game), so much the better.
Again, only one option, somewhat better but still very awkward:
Wand of Bone Talisman
If you can manage the appropriate Use Magic Device check, any item that allows you to cast the 2nd-level druid spell bone talisman would allow you to turn undead. Only one use of turn undead per casting, though, and the spell has a 10-minute casting time. A wand of bone talisman is probably your best bet, and costs 4,500 gp.
Prestige classes don’t suffer from XP penalties, which can make them a reasonable approach here.
Soldier of Light
The soldier of light prestige class from Deities & Demigods (page 208, since it’s not listed in the table of contents) should be relatively easy to enter (BAB +5 and Knowledge (religion) 4 ranks), though it does require that you worship Elishar, a deity I’d never heard of (ask your DM for adaptation in your game). Still, it grants turn undead at 1st, and divine grace at 2nd, which is pretty good. It also gets full BAB and its own Wisdom-based divine spellcasting.
Sacred exorcist from Complete Divine will advance your existing spellcasting, which is nice, and also grants turn undead at 1st. Qualifying for this class as a multiclass healer is difficult, however, as neither dismissal nor dispel evil appear on its spell list, and in any event they are a 4th- and 5th-level spell, respectively. Still, a domain icon from Eberron Campaign Setting allows you to cast spells off of a domain you don’t have, and dismissal is found on the balance domain in Spell Compendium, while dispel evil is found on the good domain.