How much money can I make if I become a computer engineer?

Really depends on location (big coast city, midwest, etc), area of computer engineering you're talking about (just vanilla software dev, embedded systems, etc), and even specific company (big tech company, small local place, etc).

Starting comp (after undergrad)

Regardless of the above, you could reasonably be expecting 60-70k starting out of undergrad. If you're talking about software at AmazAppFaceGoogSoft, total liquid starting comp (salary, bonus, stock which is basically cash at vest) is probably north of 120-140k at this point.

Career money

This will start to depend a lot on whether you are very career minded, looking to get promoted a lot, whether you decide to try for management, etc. Also the same above things (location, area, company) matter a lot. If you're 10 years in as a computer hardware engineer at a smaller place, you may still be talking 100k+. If you're a senior software person at a big but not top-paying place (Intel, HP, whatever), you could still be making 130-140+. If you're 10 years into a software job at AmazAppFaceGoogSoft in the bay area or NY or something, and have been promoted some, you could be taking in 250-300k++ total liquid comp annually.

Management can often pay more.

If you like solving problems and writing some code to do it, it can be a very lucrative career. At least, that's what it looks like now, who knows what happens if the robots start writing all of the code for us!