Pay attention to what apps are pre-installed on any new phone you buy since you can rule those out. If you find an unknown app, then seek out an expert.
You might get texts that are random strings of letters, numbers, and other symbols. It could be another phishing attempt, or a sign that spyware is on your phone.
If your phone is hot to the touch while idling and it processes even the simplest of requests at a glacial pace, you should bring it to a repair center as a precaution.
Not all spyware-caused unusual phone activity is limited to phantom notifications. If it happens consistantly, though, you might want to get your phone checked.