Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
Seek emergency help for breathing difficulty, severe or rapidly expanding neck swelling, inability to swallow saliva, or significant bleeding.
Contact the surgical team promptly for increasing redness, worsening pain, pus-like drainage, fever, rapidly enlarging swelling, new facial weakness, voice change, or trouble swallowing.
After infection treatment, follow up to confirm that swelling and tenderness have resolved.
Definitive treatment may then be discussed once inflammation improves.
Additional follow-up may be recommended for a complex fistula, recurrent symptoms, uncertain diagnosis, or unexpected pathology result.
The article also says
During observation, report growth, pain, drainage, skin changes, or repeated infections.
Keep scheduled visits even if the lump shrinks, because temporary improvement does not mean the cyst or tract is gone.
After surgery, attend the postoperative visit to review healing and pathology results.
If pathology confirms a benign branchial cleft cyst and healing is complete, long-term testing may not be needed.
Every sign above is quoted from the sofidex article on Branchial cleft cyst. If you are not sure, err upward — it is always reasonable to be checked.