When dealing with a headache, try boiling one cup of apple cider vinegar and one cup of water in a pot. Pour into a heat proof bowl and put on the table or other safe place that you can lean over the bowl and cover your head with a towel. Inhale the steam for a few minutes to bring some relief.
The warning on mine says not to use prior to 4 months of age. My son was in his Jolly Jumper from 3 months. The directions of use are that if they can confidently hold up their head then they are fine.
Have you considered a jumperoo? My daughter has the Fisher Price Jungle jumperoo and loves it. They are supposed to be safer than door bouncers and have the activity stations to keep them entertained too. They are pricey but my daughter has been using it since 4.5 months and she's 10 months now and she still loves it more than ever.