Gout: 痛風 tung fung. painful wind.
Colchicine: 秋水仙素 chau sui sin sou. Autumn water fairy 'essence'.
Influenza: 流感 lau gam. Flowing perception.
Antiviral drugs: 抗病毒藥物 kong beng duk yuek mat. Oppose sickness venom medicinal substance ('creatures', 'things').
Diabetes: 糖尿病 tong niu beng: Sugar urine sick.
Insulin: 胰島素 yi dou sou. Pancreas island 'essence'.
Arthritis: 關節炎 gwaan jit yim. Connection node heat.
Aspirin: 阿士匹靈 a si pi ling. Nomen-praefix, official (scholar), one of a pair, efficacious / miraculous.
[Note: 炎 can also be given as 炏，because the strokes will be written in the same order. Same with 花 and 芲。]
Rheumatoid arthritis: 風濕性關節炎 / 風濕關節炎 fung sap sing gwaan jit yim / fung sap gwaan jit chim. Wind wetness nature relation node (joint) heat (blaze), OR wind wetness connection node heat.
Corticosteriod: 皮質類固醇 pei ji leui gu seun. Skin substance category solidify goodness. 皮質 pei ji: cortex, cerebral cortex. 類固醇 leui gu seun: steroid.
Indigestion: 消化不良 siu faa bat leung. Melt change not good. 消化 siu faa: digestion.
Bismuth subsalicylate: 次水楊酸鉍 chi sui yeung suen bei. Next water willow bismuth. 次 chi: next, in order, sequential. 水楊酸 sui yeung suen: salicylic acid. 酸 suen: sour, tart. 鉍 bei: bismuth.
Fever: 發燒 faat siu. Issue burning.
A sound night's sleep: 香甜寐寐瞓到自然醒 hueng tim mei fan dou ji yin sing: fragrant sweet deepsleep drowse till self pledge awake. 自然醒 ji yin sing: to wake of one's own accord.
Insanity: 精神錯亂 jing san cho luen. Essential spirit error confusion.
Antipsychotic medication: 抗精神病藥 kong jing san beng yeuk. Counteract essential spirit disease medicine.
Risperidone: 維思通 wai si tong. Maintain thoughts pass-through.
Valium, diazepam: 地西泮 dei sai pun. Earth west half.
Lobotomy: 前腦葉白質切除術 chin nou yip paak ji chit cheui. Before brain leaf "idiot" slice method. 腦葉 chin yip: brain lobe. 白質 baak ji: white material (semi-homophonic for 'idiot'). Idiot, fool: 白痴 paak chi: Unblemishedly stupid.
Straight jacket: can't find equivalent. Probably 抑制裝衣服 OR 抑制衣服 yik chai cheung yi fuk OR yik chai yi fuk (surpression clothing).
Re-education: 教正 OR 勞動教養 gaau jing OR lou dung gaau yeung. Instruct straight; labour action teach upraise.
Just guessing on that last one.
But it seems likely.
