First things first being a professional webdesigner is more than just having the software and having some tricks up your sleeve. Being a professional webdesigner means that you adhere to standards of the profession, show great skill in it and make a career out of it. If you only just got started then I think its probably unfair to say your already professional at it.
What im trying to get across by this is not to stop, just to slow down. Take your time to learn and then and only then you can call yourself a true professional.
Teaching yourself is one way, and with a portfolio of work put together your clients probably won't mind. Go into an office building of a big multimedia firm on the other hand saying you taught yourself and only a few websites under your belt might raise a few eyebrows and get yourself a few laughs.
I guess it depends how serious you want to be about it. It is always good to have a education background in ICT, Computing, Art, Media etc. before going into webdesign as these subjects will help.
Short courses are also an option, many universities and colleges will run night classes on webdesign, development and how to become a webmaster. They will always look great on your C.V.
The reason most people teach themselves instead of going through courses is because it's easier for them and because a career in web design doesn't really require any background knowledge, self teaching can be enough.
Having had a background in ICT, Computing, Media, Art and English and completed several short courses I would say it is easier to get a job then if I didn't have these skills, but would have I have still found jobs? Probably. Might they pay as high? Possibly but that's not for me to say.
Onto your second question, learning XHTML, HTML, CSS and PHP is not sufficient enough if you want to be taken seriously. Coding is only half of the web development process. If you don't know how to design your shooting yourself in the foot, "your pissing in the wind".
How a website runs, to a lot of companies and people, isn't important. Most people just care about how it looks and if it loads nice and fast, which is more the graphics side than coding.
I don't think anyone would take you on to make a website for them if all you can do is code, the coding im sure will be excellent but the design could well be severely below standards.
Entry level professional experience you ask? Work Placements. Work placements are by far the best way to get experience in this industry, but they will require some background in the placement you apply for. It will be unpaid, and require you to do free work for them, but it looks great on a CV.
Before I got into this career part-time I completeted work placements in a range of areas for a month (4 weeks, 4 different companies). A law practice, general reception work, a design firm and a software engineering firm.
Putting work placements on your resume show you have taken the time to see if you fit in with this profession and show you have general skills as well as possibly specific. Sometimes you will even be lucky enough to get paid for the work you do, or they may offer you a contract at the end of it if they are impressed. They will at least provide you a reference will be very useful later on.
Any more questions? Feel free to ask.
Regards,
Jonny.