Members are more than welcome to self suggest their own art work for a Daily Deviation, in fact many CVs highly encourage self suggestions. While self suggesting may have been something people frowned upon in the past, this is thankfully no longer the case as we all recognize the need for self promotion in the competitive world of art.
But suggesting my own work is embarassing
There is no shame in trying to get yourself and your work seen. By self suggesting you are merely looking to gain more exposure from a broader audience. Look at it this way, if you're not willing to advertise your own work and get more clients and exposure, who will?
When we CVs receive self suggestions we treat them the same as we would any other suggestion so you can easily treat a self suggestion the same as you would a submission of your art to a group so more users can see the piece. While we do not guarantee that we will select your suggestion as a Daily Deviation, nobody will look down on you as if you've done something unspeakable. If your piece is chosen we don't list you as the suggester so nobody but you and the CV would even have to know that it was a self suggestion.
Things to consider when Self Suggesting
While most of this applies to any type of Daily Deviation suggestion, it never hurts to go over the basics again.
Before suggesting your piece have a look at FAQ #18: Who selects Daily Deviations and how are they chosen? to figure out which CV to send your suggestion to. Please also remember only to send it to one CV (given there are more than one who look after that gallery).
It's always a good idea to read over the CVs DD suggestion guidelines before suggesting. Some CVs have certain preferences and reading their guidelines can help you know if your piece is likely to be accepted by them as well as how the CV prefers to get suggestions (do they like an explanation of why you feel the piece should be a DD etc).
If you have received a DD within the last 6 months, you will need to wait to suggest your piece since we can only give a DD to the same artist every 6 months. FAQ #313: How can I find out if someone already has a Daily Deviation?
If you have never suggested a DD before it might be worth having a look at this in depth tutorial on DD Suggesting; So you want to suggest DDs by alexandrasalas
Now that you should have a basic idea about self suggesting DDs, for some first hand insight I recommend having a read of ChewedKandi's journal entry about self suggesting Self Suggesting DDs.
Astralseed and alexandrasalas