Welcome to APUG Katelynn,
I think a career in photography using the analog process is totally doable. You must understand that photography careers today are very competitive, weather it's digital or analog. It's hard work and requires more skill in handling budgets, clients, and marketing than making photographs. I have found that consumer clients really don't care that much about how you make your images, so portrait photography using film has been no problem with me. Commercial or editorial clients want a fast turn around but I have found that the lab is the bottle neck, not using film. Digi shooters are there own lab and deliver a file. I have found that if I am my own lab with my film my turnaround is more that sufficient for my commercial clients that I have. I don't have to do all the computer work with a film scan that I would normally do to a digital RAW image so that saves a ton of time too. For me film gets me there faster.
If I come across a potential client that want me to burn a CD right there after the shoot I don't take the job. That is not the type of client I want to work for. Be choosy who do work for and what type of work you do. People will hire you to produce work based on what you have done in the past. If you have to wait tables to pay the bills then that is something you need to consider.
I would start with a Business to Consumer model. That would be portrait work, wedding work, and fine art work. Then with a style and a portfolio of that work you can market it to commercial clients.
Hope that helps. Chase your dream!