Based on the history and photo, this does appear consistent with a mucocele (a mucus-filled cyst from a minor salivary gland), which commonly occurs on the lower lip after repeated lip biting or minor trauma.
Unfortunately, there is no medication that reliably removes a mucocele. Many resolve spontaneously over a few weeks, but some repeatedly shrink and refill, which matches your description.
Next Steps
Avoid lip biting, chewing, or squeezing the swelling.
Do not try to puncture it yourself.
Maintain good oral hygiene.
If it persists beyond 2–4 weeks, increases in size, recurs frequently, or interferes with eating/speaking, consult a dentist or oral surgeon. A minor procedure may be needed to remove the cyst and the involved salivary gland.