What to do about a stuck chain link on 10 speed chain
Right solution is to use the "tight link removal" position of most chain tools:



Just choose the side where the pin is showing most outwards, and pull it in a tiny bit. This is very subtle, and your link will be released.

An alternate solution is to grab the chain with both hands (dirty!) and force it as if you were to bend it sideways, in both directions. This always works and is very quick, but is not very elegant.