Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
With the common cold, you may not break your fast unless the cold is unbearable for you and you cannot function properly without taking medication.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
You may break your fast only if fasting makes your illness worse or prevents you from taking medications you must take for the treatment. With the common cold, you may not break your fast unless the cold is unbearable for you and you cannot function properly without taking medication.
If you think this is the case, then you should break your fast, for Allah says: “Hence, whoever of you lives to see this month (i.e., Ramadan) shall fast throughout it; but he that is ill, or on a journey, [shall fast instead for the same] number of other days. Allah wills that you shall have ease and does not wish you to suffer hardship; but [He desires] that you complete the number [of days required] and that you extol Allah for His having guided you aright and that you render your thanks [unto Him]” (Al-Baqarah 2:185)
Almighty Allah knows best.