New iPhone started to charge really slow after two days usage

claim a warranty as it should have at least a 1 year guarantee.

Have you tried to replace charging socket?

I agree with Synced Repairs, but if you didn't want to take it back without trying some things then you can;

1. Make sure you use a 12w adapter to charge the phone, and a decent lightning cable

2. Do a software reset - Just press and hold both the Sleep/Wake and Home buttons simultaneously for at least 10 seconds, until you see the Apple logo. You can let go of both buttons after the Apple logo appears.

If that doesn't work, take it back to an apple store and they might just give you another phone (if it's the first time you've gone there).

Hope that helps :)

I would say your best bet is to try a different cable and plug to be sure it isn't due to either of those. Then bring it into the apple store for diagnostics. If they can not determine issue I would check back with where you purchased the phone and ask for an exchange. It may be a bad connection as that is not normal.