Is there a reason you are transitioning to a 4 hour routine at 3 months? Is your LO closer to 4 months? The transition can take a few weeks.
This may seem like an obvious question, but are you feeding your LO when he wakes? Is it hunger? Do you see any signs of discomfort?
What is your routine like during the day? Can you post it in EAS format?
You are doing the right thing by patting your LO back to sleep during naps. This is very frustrating and can take a bit of time. But it is teaching your LO to sleep.