Spout problem on old double handle faucet
If your spout pivots where it meets the main body, there may be athreaded coupling ther which you can loosen and remove the actual spout portion. If it comes off take it to a plumbing specialty shop that has been around a while.
If not, examine the aerator or what is left of it. If it is female and the thread of the spout itself is not damaged you may be able to soak it with a penetrant or lime buster and desolve corrosin and peel away the remaining aerator. If it is a male thread it will be a bit more tricky to remove from below and inside.