What about the Alla Seltzer Cold med? It has an antihistamine in it and those work similarly on the brain to the way antipsychotics do.

You cannot mix it with an MAOI and it has sodium in it, so I don't know how it would mix with lithium.

ACTIVE INGREDIENTS
Aspirin 325 mg (NSAID)* (Pain reliever/Fever reducer)
Chlorpheniramine Maleate 2 mg (Antihistamine)
Dextromethorphan Hydrobromide 10 mg (Cough suppressant)
Phenylephrine Bitartrate 7.8 mg (Nasal decongestant)
*nonsteroidal anti-inflammatory drug

Not sure what meds you already take. I would call my doc and ask for recommendation or speak to the pharmacist.

If it were me, I would lean on essential oils.
A Guide to the Best Essential Oils for Winter & Fall - Dr. Axe
How to Use Essential Oils for Colds