Thanks for writing your query.
After reading your post, it seems that you had suffered from severe hypothermia
when you were in cold enviornment. It is seen that after severe hypothermia, if active treatment of external warming is done, it can result in sudden drop in blood pressure along with low cardiac output
. This condition is known as Rewarming collapse or rewarming shock. This can result in headache and episode of fainting due to low blood pressure. Internal warming like drinking hot beverages is more safer than external warming.
You can take pain killer like paracteamol for mild pain or ibuprofen
after meals for more severe headache
which has resulted due to fall.
Also keep your body warm and avoid going to cold for prolonged periods
without adequate protection. Give rest to your body for speedy recovery.
If the problem persists, you can go to the E.R. for medical examination and vitals recording.
I hope this is helpful to you.