Swallow's Nest is a Quick-Play Spell Card.
Spell Cards are usually activated from the hand on your turn unless their type gives another timing window.
On the current TCG and OCG Forbidden & Limited lists tracked here, Swallow's Nest is Unlimited.
YGOPRODeck lists Swallow's Nest for these formats: Duel Links, Common Charity, Edison, TCG, OCG, Master Duel.
A listed print of Swallow's Nest appears in Hidden Arsenal: Chapter 1 (HAC1-EN171) at Common rarity.
Among markets shown on this page, the lowest listed snapshot for Swallow's Nest is about $0.40 on TCGPlayer (prices change frequently).
