yes you need to take good care of your back since you said you are having pain while coughing it might be chances of having PIVD you need to get your
MRI done for your lower spine. and few thing you need to take care
1-avoid forward bending
2-avoid lifting heavy weights
3-drink lot of water and have fibrous diet to avoid
constipation as it may increase your backpain.
4-wear back support while walking
5-avoid brisk walk and even a walk also for few days till pain sbsides
6-apply hot pack thrice daily for 15mins on lower back also on hips
7-take pain killer for few days
8-after your MRI done get your
physiotherapy also to avoid further complication
9-alwaz take side turn while getting up from bed
10 no high heels or too flat shoes.Wear comfortable foot wears
11-consult a doctor asap