We aren't trying to cut you down, but do realize that it's different to be a "no experience necessary" candidate coming in to take a studio's training program and then teach than it is to be someone who has years of experience learning and competing that they've gained before starting to teach. Reputations are vitally important in the ballroom world.
If you want to teach ballroom dancing and are more interested in teaching absolute beginners, low-level group classes, and "wedding couples" who come in to just get that one dance for their big day, then going through a "no experience necessary" program will work just fine for you. If you want to make it as a competitive professional who does well in pro competitions and who can also attract higher-level students then you are at an automatic disadvantage by starting at age 23 and starting teaching without ever having an amateur career of your own. This is not cutting you down, this is just the facts. The top pros all started to dance ballroom/latin in their early teens or earlier, and gained thousands of hours of experience dancing and competing before they ever got started teaching.
It is possible with a lot of work to start in your 20's and go far. I can think of two men who started in their mid-20's who have gone on to become US Rising Star Champions in the past couple of years. There are others who also started in their 20's with "no experience necessary" who have developed in to sought-after teachers who are excellent dancers. It's hard work and not everyone will succeed, but so long as you have an idea of what's ahead of you then it's up to you to choose your path. Which brings me to my next question:
Another question I have is that if you've got a clear idea yet of what the life of a ballroom dance teacher is like. If you've just started lessons you might not see beyond the 'glamour' yet. The hours are long, the pay is low unless you are one of the top instructors in your area, and the work is hard on your body. I know several people who loved to ballroom dance who became teachers -- and who never dance socially anymore because by the end of the week they are so tired from teaching and practicing that it's just not fun any more for them.
It's very important to check out the policies of the studio where you'd take those "no experience necessary" lessons. Do you pay for your training, or do they? Are you locked into a contract after taking the lessons, or can you go apply for jobs on your own? What will the pay rate be? Sure, a student might be paying $65/hour for the lesson, but the teacher might only be keeping $20 of that and the rest goes to the studio.
And then there's the realities of finding a partner. It is the most difficult thing about ballroom/latin dancing. It seems no matter what your level it's not easy, and that it's even harder if you're a pro.
Personally, I think it might be a good idea if you had a little more time in the ballroom world before deciding this is the career for you. Go to a couple of dance competitions and look at the level of the competing pros. Make inquiries to try to find a partner. Talk to teachers and find out how they feel about their jobs. Maybe this is the career for you, maybe it's not, but be aware that it's a difficult one and there are many pitfalls.