My mother tdap vaccine yesterday and there is lump which developed today. Is it some thing normal or do we need to take any medicine to avoid it?

Common. The vaccine is injected into muscle, which can develop such a lump lasting a few days in response. You can ignore it or treat it with comfort measures. It is no considered a worrisome reaction.
Swollen arm. Put cold compresses on her arm for20-30 minutes several times a day to reduce the swelling.
This is normal react. This is a normal eaction to tdap vaccine in some people and you can put ice on it locally for 48 hours and it will go down by itself.