My mother is allergic to codeine, she will bbe having back sugery soon. ... What can she suggest for post op pain that would be just as effective?

What is allergy? If it's nausea or itching, then she may experience that with all opioids. But people all have different metabolisms and sensitivity so maybe norco/vicodin may work. Codeine gets metabolized to morphine specifically, which tends to have more itching. Maybe try lyrica/neurontin since may be nerve regeneration component. Never seen it used on post-op wound but Lidocaine patches are available.
Depends on allergy. Side-effects of all opioids can include itching, sleepiness and nausea. A true allergy can include rash, airway swelling and extremely low blood pressure. Non-opiate medicines such as toradol and Acetaminophen can help reduce the need for opioid and lower their side-effects. However, a true allergy will need to be further evaluated.
Nausea? Do you mean she gets nausea? That is not an allergy. Codiene like all narcotics causes motion sickness. Prevent by avoiding narcs with tylenol, (acetaminophen) nsaids, ketamine, local anesthetic/blocks, gabapentine, and steroids. Prevent nausea from narcotics by scope patch #1, Droperidol #2 antihistamines #3, compazine/phenergan #3. 5ht's are no better than placebo wasted money. Ask for md with low nausea ratte.
No nsaids. Nsaids post back surgery are a bad idea due to decreased wound healing. They are contraindicated for up to a year after a fusion. Other oral pain medications will be fine most likely even with a Codeine allergy.
Other pain medicatio. A "true" allergy to codeine (meaning anaphylaxis) is rare. Usually, patients may think their allergic because they get itchy, nauseous, may get a rash. Unfortunately, the other 'opiate" medications may cause the same thing. Still their are other choices. Express concerns to your doctor though about this, with the amount of different classes of drugs, there will be one for her.
Follow doc's advice. Many surgeons have a pain protocol for their pts. If (s)he/ anesthesiologist know about her allergy, they will have alternate pain meds to use. Make sure it's truly an allergy: unset stomach is common side effect of codeine; allergy usually involves rash or hives or swelling of tongue/throat & difficulty breathing.
IV meds, Tramadol. You should let the doctors know of her allergy to Codeine if it's not already documented. During the hospitalization, she will probably get IV pain medications like morphine or fentanyl. After she is discharged home, oral medications like tramadol combined with an NSAID like prescription strength Ibuprofen could help.