Dr.Kadwa please advise

If you feel better from wrapping head up or from warmth your remedy is hepar sulph 30c.
If you desire open air and don't like warmth your remedy is pulsatilla 30c.
Please take three doses of indicated remedy daily at a gap of 4 hours for two days and report back.

Please take three doses of hepar sulph 200c at a gap of 4 hours on a single day. On next day onwards you may take 2 tablets each of ferrum phos 6x and kali mur 6x.

Other members of your family may take following remedies as a preventive measure.
For those who are restless should take three doses of arsenic alb 30c at a gap of 4 hours for one day.
For those who suffer from drowsiness and dullness should take three doses of gelsemium 30c at a gap of 4 hours for one day.

One dose is 3-4 pills under tongue until dissolved or
3-4 drops of remedy in some 20 ml water.

..On next day onwards you may take 2 tablets each of ferrum phos 6x and kali mur 6x thrice a day at a gap of 4 hours..

For cough you may take bryonia 30c thrice a day at a gap of 4 hours for 2 days. Other members of your family may also take bryonia 30c for 1-2 days depending on severity of symptoms. In my opinion it can also act as a good prophylaxis against Flu.
You are also suggested to do the following to overcome cough.
1. please take 1 tsf sitopaladi choorna in the morning and evening.
2. please take 1-2 pieces of Kali mirch and chew as much as possible before swallowing. It is a specific and unquestionable remedy of whooping cough. Piper Nigrum (black pepper) also appears on page 520 of Boericke's MM. This is to be done whenever you have bouts of cough. It would be better if you could also have mulethi and mishri alongwith kali mirch.
These two options will not antidote or dilute the action of homeopathic remedies.
3. Cell salts as recommended earlier are also effective in controlling cough.

Please advise can arsenicum follow gelsemium if the symptoms have bcom mild after gelsemium coz some of family members are still showing signs of lethargy and slight fever in the evenings.

These two remedies are not related ie neither do they antidote each other nor these two remedies are inimical. Similarly the table of Relationship of Remedies does'nt say that one follows the other well. Therefore there is no problem if the patient who is on gelsemium moves on to Arsenic Alb. But as i have told earlier for lethargy without restlessness Gels is better and for lethargy with restlessness Arsenic Alb is better.

And can bryonia be taken along with ars?
i think that this question is with reference to your sister who is injured. She should not take arsenic. Bryonia alone is sufficient.

till wen do i take fer phos and kali mur?
It is is not clear what you want to say. Any person may take ferrum phos and Kali Mur if he has flu like symptoms. It is better to follow up with tissue salts when the patient gets only partial relief from homeopathic remedy.