This is likely due to your location and services coverage.
since you have a fairly new iPhone, the device is fully capable of 4g connection from itself.
you might live at a location with weak lte signal, thus the phone frequently fall back to 3g. Or it failed to revert back to lte once a phone call ended.
If your phone switches between 4G LTE and 3G networks when not in use then you have a weak 4G LTE signal. It's possible you have a poor connection to the network. Toggling airplane mode on/off will re-establish a better connection if that's the case. If someone else in your household has an Android phone you can check the signal strength in their phone settings. iPhone does not have this option.
In an Android phone go to Settings>>About phone>>sim card status>>signal strength....mine hovers between -100dBm and -105dBm which is okay ( I have no issues.) That reading for the 3G network is worrisome. If its below -110dBm then its not surprising you have issues. Normally you would want it -95dBm and above whereas my 3G network signal is around -65dBm whuch us excellent.
So there you go then. It's your phone or your area. These new 4G plans are about speed, not connection.
I was recently somewhere very rural that barely got reception. It would drop itself down to HSPA when I turned on data. Where I live is quite urban. I get 2 bars just sitting here resting on 4G. It shoots up to full bars when a call happens.
Are you meaning up top on the status bar?
Before you changed plans did it always say 4G or LTE or did it also flip back and forth between 3G and 4G? Remember that this place has always been on 4G. It's just that the speed was throttled down to 3Mbps and they marketed it as so-called 3G. Maybe you're in a somewhat weak 4G area and so the phone is scrambling to connect to something and it finds 3G or HSPA.