I would stay away from the green tire slime tubes. There is another product call Stan's NoTubes that is used in tubeless tires. Tubeless tires require a specific tubeless tire as well as a rim. The draw back to this method is you will need to replace the sealant about every 6 months or so as it slowly congeals over time.
I have put the Stan's stuff into tubes before, but given the fact that you only get about 6 months to a year out of the sealant, you would still be replacing tubes every year.
You really should not be having the issues you are with flats. It sounds to me like there is something else going on. Read through the following steps then go through them IN ORDER and see if the problem persists.
1. Once you get a flat, use a proper plastic tire lever (not a screwdriver or any other metal object) to remove the bead of just ONE side of the tire. Make sure the valve stem stays in place in the valve stem hole on the rim.
2. Hold the valve stem in place with one hand and use the other hand to pull just the tube out of the tire on the side you removed the bead from the rim.
3. Use a bike pump and fill the tube with enough air that it just about doubles in size. Don't worry, it takes a lot more air than that for it to explode when it is outside of the tire. The "exploding tire" from over inflation is most often caused by tire bead or rim failure. A gap forms and the tire "squirts out" through this opening and rips leading to the "explosion." Inflating a tube that is outside the tire to twice the size of the wheel is really only filled with maybe 6-10 PSI, well under the breaking point of the tube.
4. Now you are going to methodically dunk the over inflated tube in a bucket of water one bit at a time until you find the hole.
5. Mark the location with a silver sharpie or a piece of tape.
6. Let enough air out of the tire that it is about the same size as the tire.
At this point, you should be holding a wheel with a tube hanging out of the tire and one side of the tire bead off the rim. The tube is marked where the hole is. By leaving everything in the same position it was when the flat occurred, you now have a good idea about the area of both the tire and the rim that need the most attention for the cause of the flat.
Where the hole is at on the tube is important. If the hole is in the "inside"of the tube, then you might need to replace the rim strip. Gorilla Duct tape is great for this purpose. Remove any old rim strip/rim tape material and give the wheel 2 layers of gorilla tape. I actually cut a roll of tape just as wide as the rim is from outside braking surface to outside of braking surface. This gives just a little extra tape that can wrap up the side of the rim bed.
If the hole is on the "outside" of the tube then you most likely have a small piece of metal in the tire. When you inflate the tire, the pressure actually presses the small piece of metal into the tube. Sometimes this can take a while to notice the problem depending on the size of the metal sliver.
If the hole is on the "sidewall" of the tube, many times you might find a matching hole on the other side of the tube. This is what is called a pinch flat. A pinch flat happens when a tire is ridden under inflated. A rock, crack or bump causes the tire to compress, pinching the tube and tire between the edge of the rim and whatever you hit on the road. This commonly causes 2 small holes in the tube called a "snakebite" The remedy in this situation is proper inflation.
That brings me to the final point: Tire pressure is something that needs to be checked before every single ride. The rubber that is used for bicycle tubes is not 100% air tight. On a microscopic level, air molecules can and do escape through spaces between rubber molecules. I also have a road bicycle and I run those tires at 95 PSI. The next day, the gauge will read anywhere between 90 and 95. If I go long enough between filling the tires, they can and have dropped below 40 PSI. It's just like party balloons. They don't hold air forever. Filling the tires before you leave the house for a ride takes just a few seconds and can save you lots of frustration and money later on.