The 1886 liberty Head Half Eagle is a common coin. And from your description the likely value is $300.00 to $350.00. For an accurate assessment of value the coin needs to be seen and graded. Coins that are bent, corroded, scratched, used as jewelry or have been cleaned have far less value if any to a collector or dealer.
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Yes. This coin is called a Walking Liberty Half Dollar.
Below the eagle on the reverse.
The Liberty Half Dollar - also called the "Barber" Half Dollar - has an image of Liberty's Head with the Eagle Crest image on the reverse, and was minted from 1892 to 1915. The Walking Liberty Half Dollars - or "Walkers" - show an entire Liberty's body walking, with a reverse showing a side view of an eagle perched on a rock, and was minted from 1916 through 1947.
The 1922 is probably a peace dollar. It would have the word peace on the side with the eagle. The 1921 is probably a Morgan dollar. It has a Liberty head on one side and an eagle on the other. These are worth about $25-35 on average.
Is it a Morgan or Peace dollar? A Morgan dollar features a personification of Liberty with a crown saying "LIBERTY" on it. A Peace dollar has a personification of Liberty with rays of light coming out of her head. The reverse of a Morgan dollar has an Eagle with arrows and an olive branch and a wreath under it. The reverse of a Peace dollar features a perched eagle sitting on a rock inscribed "PEACE". Without knowing the type of coin, it is impossible to state a value.