Pipe bursts...very small holes...advice?

Hello...thanks is advance for anyone who can help point me in the right direction...

I live in an older house, with barely any insulation. I wrapped all of my exposed pipes, kept the taps dripping, left the cabinets open inside...pretty much everything they suggest on the news here when it reaches the 20s. Unfortunately in my garage ceiling coming from my water heater were uninsulated pipes that burst. They are 2 very small holes, I would say the size of a pencil eraser. I have galvanized pipes. The water is currently off and I drained the pipes via the faucets inside.
My question is: Is there anyone to plug the holes in a safe, actual way that will work and will not cause any more leaks? If so, how long do these methods last?
Also, once I fix it, how do I keep it from happening again. There is no access in the ceiling except the giant hole where you can just see a few feet of pipe.
Someone I know said I could buy this waterproof putty, let it cure, and put a pipe clamp on it and that it should last a year or so. I'm on a limited budget, so if I can do the job myself until I can afford new pipe and plumber it would be great. At the same time, if I have to use my credit card for a plumber I'd rather know before I buy everything to fix it.
Thank you!!

Take some sheet rubber and a hose clamp.
Or you can buy a repair clamp that is rubber lined, that clamps over the galvanized pipe.

I'd use "JB Weld". It takes time to cure, read the package carefully. It sets up in 30 minutes, but takes a good 12 hours to fully cure. I believe in belts and suspenders, so I would wrap a piece of an inner tube or tire patch on there over the repair and put a couple automotive radiator hose clamps over it. I once was inspecting above ceiling and saw a pipe with about 50 of these repairs on it!

To keep it from happening again, you need to heat the garage above freezing when it gets cold. I use a kerosene heater but that can be dangerous; if you have gas fumes in there it's not recommended, although if you elevate the heater, gas vapors are heavier than air. For Houston, you could probably get by with one of those plug-in electric radiators.

Note, insulating pipes will not prevent freezing. Insulation simply slows the time it takes to freeze. Placing insulation between the pipes and the freezing condition will help if there is a heat source on the other side of the pipes.

Thank you so much for the advice. I've stop the leak and there is not water coming from the pipe anymore. Everything works in the house, except my bathtubs are not having any hot water flow. The sink still has hot water. When I turned on the tub the water came out all brown, trickles to a stop, and you can hear air. Any thoughts? As far as I can tell, there are not any leaks.

edit: now there is no air sound at all. Just silence.