What can happen if I take half of Zofran with Wellbutrin?

Interactions between your drugs
Major
buPROPion ondansetron
Applies to: Wellbutrin (bupropion), Zofran (ondansetron)

Using ondansetron together with buPROPion can increase the risk of a rare but serious condition called the serotonin syndrome, which may include symptoms such as confusion, hallucination, seizure, extreme changes in blood pressure, increased heart rate, fever, excessive sweating, shivering or shaking, blurred vision, muscle spasm or stiffness, tremor, incoordination, stomach cramp, nausea, vomiting, and diarrhea. Severe cases may result in coma and even death. You should seek immediate medical attention if you experience these symptoms while taking the medications. Talk to your doctor if you have any questions or concerns. Your doctor may already be aware of the risks, but has determined that this is the best course of treatment for you and has taken appropriate precautions and is monitoring you closely for any potential complications. It is important to tell your doctor about all other medications you use, including vitamins and herbs. Do not stop using any medications without first talking to your doctor.

Source: https://www.drugs.com/interactions-check.php?drug_list=1752-1120,440-203

Now, if the same Dr. prescribed both medications, he/she most likely is aware of the potential interaction and outweighs the benefit is greater than the risk. If this is not the case and 2 different Drs. prescribed the meds without knowing you are on 1 or the other then inform them.
And last but not least, do not self medicate, inform your Psychiatrist you are planning on taking Zofran, but do not take any until you clear it with your shrink first.

Wishing you the best, masso