Should I use TINYINT for ID (PK) field in MySQL?
Yes.  You should also say UNSIGNED:  TINYINT UNSIGNED.  Range 0..255; 1 byte.

Actually, it is such a tiny optimization that I don't bother mentioning it.

Think about using the smallest datatypes when you first CREATE the table; it is messier to make the change later.

SMALLINT UNSIGNED:  0..65535, 2 bytes
MEDIUMINT UNSIGNED:  0..16M, 3 bytes
INT UNSIGNED:  0..4B, 4 bytes

Keep in mind that certain operations "burn" AUTO_INCREMENT ids.  This could lead to an unexpected overflow.  Examples:  INSERT IGNORE and REPLACE.  They may preallocate an id before realizing that it won't be needed.