Can I get free relief if my ball is plugged in its own pitch mark?

Yes, if it's in the general area (Rule 16.3).

When it counts as embedded: the ball is in its own pitch mark made by your previous stroke, and part of the ball is below the level of the ground.

How to take relief:

• The reference point is the spot right behind the ball.
• Drop in a relief area one club-length from that point, in the general area and not nearer the hole.
• No penalty.

When you can't take relief:

• The ball is embedded in sand in a part of the general area that isn't cut to fairway height or less.
• The ball is in a bunker or penalty area (Rule 16.3 only covers the general area).
• Interference is only from something clearly unreasonable, or playing the ball as it lies is clearly unreasonable because of something else (for example, it's plugged under a bush).

On the putting green, you can repair the pitch mark under Rule 13.1c instead.