Was prescribed omeprazole 40 g for a month, then started nimesulide for sore throat. Now heartburn is back. Can NSAIDs cause reflux?

Yes. NSAIDs are known to cause problems with gastric reflux and heartburn. If you have to take them do so with food and lower doses if possible. Please see your primary care to ensure that exact cause is figured out for the reflux.
NSAIDS. These agents irritate the lining of the upper GI tract and potentially increase the symptoms of acid reflux. The most serious side effects are ulcers, bleeding, kidney failure, and, rarely, liver failure. Be careful. You should be tested for Helicobacter pylori and treated if it is present. Best wishes, hope this was helpful.

Related Questions

On 80mg. Omeprazole for 5 days with no change in mucous or sore throat. Worse after I eat. Any ideas? Don't have heartburn at all.

Post nasal drip. Omeprazole is used to reduce stomach acid, thus reducing heartburn. It will not affect mucous which is probably post nasal drip causing your throat to be sore. You'll need to figure out if the mucous is a result of allergy to pollen, a cold or perhaps sinus infection, and treat accordingly.