Carried something heavy 1day ago, arm feels like it's burning, weak, somewhat inflamed. did i sprain/pull something? any home remedies?

Neck strain: You might have strained your neck in such a way that your nerves are inflamed. I would see if it stays that way or gets better. One common advice is to ice the area, if the inflammation goes down with just ice, great. Otherwise i would see someone who can help heal the area.

Possible neuropathy: Neuropathy can happen as a result of trauma, or nerve damage due to the consumption of alcohol or certain medications. Symptoms can range from a numbness and tingling sensation, possibly a burning sensation, to an uncomfortable painful sensation of the extremities. Get evaluated by a professional to determine the exact cause in order to get the appropriate treatment.