Your symptoms would be consistent with persistent rhinitis/rhinosinusitis that can also cause upper airway problems with secretions from the sinuses.
The SLE in the background would mean you are either on steroids or immunosuppressants and therefore fungal rhinosinsitis may required to be excluded.
A CT Paransal sinuses is recommended.
The treatment would involve: long-acting oral antihistamines with fluticasone
or mometasone nasal spray
2 sprays per nostril twice daily.
The link with SLE is possible particularly if it is active, and blood tests such as complete hemogram, LFTs, C3 C4, dsDNA levels would be required, and the condition is SLE related angioedema
of the upper airway. Your Rheumatologist
would be the best person to get in touch with if the tablets and nasal sprays do not help.