Paracetamol - for fever and pain
Antacids tablets - for Gastritis
Diclofenac gel or equivalent - can apply over joints or painful areas (for joint pain and muscle pain)
Silver sulfadiazine or equivalent - to apply over small burns before proper medical treatment
Oral rehydration solution - to hydrate, specially during diarrheal illnesses
Chlorhexidine mouthwash - an oral antiseptic, can use for oral ulcers
Potassium permanganate - an antiseptic to clean wounds
Povidone iodine - an antiseptic solution or cream. To apply over wounds or ulcers
Plasters
Gauze swabs/bandages
Cotton swabs
Isopropyl alcohol - to clean wounds
Pair of Scissors
Antihistamines and antiemetics through your family doctor
Antihistamines for milder allergies and rhinitis
Antiemetics for vomiting
You need a prescription to buy those two drugs and ask your family doctor for further information/advice.
Those mentioned drugs/medicins only to be used as first aid. Always seek medical care.
Always consider existing allergies before use.
If anything else, I'll edit the post later.
New additions
A tweezers
Hydrogen peroxide - to clean wounds
Thermometer
Disposable gloves
Ice pack