What are the essentials to go in a travel sewing kit and a travel first aid kit?

Sewing kit:
Some thread, needle (or two), safety pin, small scissors, and if you really can sew, pins, thimble and needle threader.

First aid kit, more difficult.
Some plasters/band aids, some bandages, alcohol wipes, some pain killers. Many people want to take some medication that will help with upset stomach.
If you go to a country with poor health care, specially one in the tropics, make sure you have an approved kit, with all that is advised by the medics, too important not to.
But if you just go to a western country and stay in the populated areas, you need to take no more than you would take to work every day.

Sewing kit: start with an empty dental floss box or an altoids box. Add: 2-3 embroidery needles (large eyes, easy to thread), a 4 to 6″ piece of iron-on tricot interfacing like Fusiknit, preferably both black and white — this can be bonded with an iron to the inside of a tear or hole that develops. On folded paper or thin cardboard, wind about 15 ft of colors of thread that will go with the colors of clothes you’re taking with you. I usually carry black, white, red, and a medium grey that will blend with most medium colors. Add a few buttons of the size and color (roughly) used on the clothes you’re taking, a couple of tiny safety pins, a couple of medium safety pins, and a large safety pin and a wrapped single edge razor blade.

If you’re using an altoids box, you can usually get most of a first aid kit in there, too… a few bandaids, some Compeeds for blisters, a small tube of ointment like Neosporin or Bactine, and a couple of “wet” hand wipes like you’d get with a carryout restaurant meal. Toss in a small pair of tweezers. That’ll get you through most of it.

Also, if you’re using an altoids tin, slice down through about 3 layers of duct tape to make a patch of duct tape a little shorter than the size of the bottom of the tin. Stick the three layers of duct tape to the bottom of the tin — it’s emergency luggage hole repair, shoe repair, even first aid for a bad cut till you can get better materials.

In a separate container, like an old pill bottle or even tucked into the lining of another bag you’re carrying, toss in a few ibuprofen or whatever your favorite painkiller/headache remedy is (ibuprofen is more effective on muscle spasms and is a better anti-inflammatory than aspirin or tylenol/paracetamol, so that’s what I carry), and some of your favorite upset stomach/diarrhea remedy (I carry Peptobismol caplets or tablets). A few Benedryl (diphenhydramine) tablets can be useful for allergies or as a “sleeping pill” — but if you’ve not tried this medication before, try taking one on a night when you don’t have to get up the next morning — it leaves many people pretty groggy the next day.

Also carry a couple of clean bandannas or cotton scarves in your luggage, and one rolled around your first aid kit. Bandannas can be washcloths, towel substitute, halter top, sling, luggage id, pillowcase, handkerchieff, sleep mask, and a dozen other things. Lightweight, easy to wash by hand, usually dry overnight.