You asked

Should I have a bedtime routine for my baby?

Babies respond very well to a bedtime routine.  The routine can be whatever works best for you and your little one.  The key is to stick to whatever routine you decide upon.  Try to keep your bedtime routine relatively simple. You want to establish a routine that you can use even if you are not at home. Also, if your baby ever spends the night at their grandparent's house, you want someone else to be able to follow your routine. The primary focus of any successful bedtime routine should be to create a feeling of calmness.  It is not the time to play rowdy games. 

Consider giving your baby a warm bath or shower before bed.  Warm water has a soothing effect. You could also incorporate a specific smell such as a certain soap or lotion, music, a special book, a special blanket, a special bedtime song, a nightlight or a massage. Be sure to include a feeding in your routine. Be careful not to include too many steps in your bedtime routine as you don’t want to over stimulate your baby right before bed.

More questions

Concern over give infants cold medicine
MummyPages mums tell us where to get the best Christening gowns in Ireland
Buying clothes for a newborn? Here is what you need to know
It is recommended that you seek advice from your GP when the colic or persistent crying begins. 
The persistent nature of colic means that there are likely to be times when your baby cries, whatever you do.
If your baby cries excessively, but otherwise healthy and feeding well, it is quite possible that he has colic.
How to know if your baby has colic
There are several types of eczema but Atopic is the most common in children
There are various causes of eczema in children
Here are the symptoms your should look out for if you think your child has eczema