No. It will not damage or affect the phone or SIM. If you have any problems, go back to your old APN (or other). The only thing changing the APN can affect your ability to send/receive MMS and the data speed (which you are already seeing improvement).
Read moreDoes the APN matter?
Your mobile carrier scans your APN settings as a means to generate an IP address. Additionally, an APN is required if you want to connect to the correct secure gateway or a private network such as a VPN . It is not only a means of connectivity; an APN is also extremely essential for security and privacy.
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