Serious issues after Apple Store changed the battery

My iPhone SE (1st Gen) had the battery change at a local Apple Store on 59th and 5th 2 days ago. I fully charged around mid night last night and did not use it. This morning, around 8:00, when I woke up, the battery was already completely drained.

The battery gets extremely hot when charging which is dangerous, not supposed to be for a new battery.

My touch screen which had been working properly before the battery replacement is behaving strangely with frequent delayed responses.

I went to the same store and they insisted the touch screen issue had to do with software which sounded suspicious as the issue did not exist before the battery was replaced. They also had no meaningful answer for the heating up when charging.

Instead of having the repalcement done by a third party for much less money, I went to the Apple Store, but now my phone is worse than before. What is my recourse? Please send me your advices. Thanks.

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