CanI sue my bank for depositing $1000 into someone else’s account and not mine?

You could sue the bank for negligence.  Negligence is the failure to exercise due care (that degree of care in this case that a reasonable bank would have exercised under the same or similar circumstances to prevent foreseeable harm).

In order to prove negligence, you will need to prove duty (of due care mentioned abpve), breach of duty (failure to exercise due care by depositing the money in the wrong account), actual cause, proximate cause and damages.

Actual cause means but for the bank teller would the money  have been deposited in the wrong account?  If the answer is no, which appears to be the case, actual cause has been established.  Proximate cause means were there any unforeseeable, intervening events which would relieve the bank of liability?  If the answer is no, proximate cause has been established.

Damages means the amount of compensation you are seeking to recover in your lawsuit.  Your damages would be the one thousand dollars that was lost.  If the bank has corrected the problem and deposited one thousand dollars into your account, you won't recover anything in your lawsuit.  If the bank has not corrected the problem, proceed with your lawsuit.  You could file your lawsuit in Small Claims Court.  Your damages would include the one thousand dollars plus court costs.  Court costs would include the court filing fee and process server fee.