A.,
You certainly can, but like any career, it's not easy. Your options are supercuts (hourly), booth rental (buy your own supplies and rent space) or high end salon (you get about 1/2, but supplies, etc are bought for you).
The biggest thing is to build up your clientele. It takes time. Do you plan to relocate? You would have to start all over.
I'm not sure how much school is now, you would have to call, I'd guess around $14K. If you have not attended college, there are some grants, etc.
This will sound harsh: I graduated college and went straight to beauty school. It was a very drastic contrast. Highly educated professors and students to younger, high school graduates, some were still in high school. It was difficult to find a niche socially.
I started in a religious area so at least we had our faith. After 1/3 of my training I moved across the country to an area more typical with it's religious diversity. All the students in the class were very young, a number of them were already single mothers, just out of high school. Again, it was a difficult social situation. For this and many other reasons I discontinued my training at that point.
I regret stopping, but I also know I wouldn't have wanted to work in cosmetology full time.
It would take a lot of time to build a clientele that would only come on weekdays. Most of the work is when others are off work-as a mom of four I want to be home when they are home.
I have back problems and standing and leaning for that period of time would cause me quite a bit of pain (consider your own situation here).
I worked at a salon as a receptionist after I stopped school. I remember an experience where a single mother, one of our top stylists, got very upset when we didn't try to fit someone into her already full schedule. It was a financial issue. If you think you might be supporting as a single mom, look into salary estimates more extensively.
The atmosphere at the salon also turned me off a bit-almost all the stylists smoked, etc.
I apologize for writing so long, and being harsh in some areas, but I am trying to be honest and I hope it helps you as you consider this career path.
BTW it's been 9 years since school. I cut hair for my friends and family to this day and LOVE doing it very part time.
Good luck!