You describe common winter time symptoms. There is not much to do for a cold other than fluids and rest. You can try a cool mist humidifier or vaporizer in your room when you sleep. That sometimes helps. The best approach to cold is prevention. Make sure to wash your hands thoroughly and frequently.
The more important concern is your history of asthma. Cold symptoms can frequently trigger asthma attacks. Tha'ts what makes preventing colds so much more important. I hope you have the appropriate medication close by for asthma attacks if you were to have one. If you don't, you must consult your doctor.