I just wanted to say that three months might even be impatient for self-publishing standards. You'll need to find an editor, make the edits, probably more than once for proofreading, etc., have the cover mad, send material out to reviewers, etc., have the cover designed, and so on. One of the biggest mistakes people make with either self-publishing or publishing in general is to be too impatient to make sure things are done right. Everyone has done it (usually with the first book, after which we learn better), but especially with self-publishing you can do more harm than good because a flawed product will not win you any sales.
As for searching for an agent/publisher, you probably won't even hear back from many publishers in three months. Agents you will, but it might take submitting to a hundred agents, and if they want to read the full product it can take several months to hear back.
The industry is slow. That's okay. It's frustrating as an author sometimes, but that's just how things are. Add to this that even if you get an agent to speed up the process, selling to a house can take some time as well.
I'm not sure why your topic is particularly time-sensitive, unless as mentioned before it has to do with a specific event. For instance, I can see how a 2012 book would want to be published before 2012, but even in that case you'd have plenty of time to work on it in advance. Chances are you will not be any worse off for waiting six months, which is the minimum I'd give it. In that amount of time, you'll be able to craft a good query letter (absolute necessity) and you should be able to tell whether or not submissions are going well. If they do go well, you should be able to hear back from many agents in that period of time. You'll also be able to tell how you're doing. If it looks like no one is biting, then you'll have had plenty of time to get things prepared to self-publish if you choose to.
The fact is, if you have something hot it should be picked up quicker, but even then it can take time. You just have to consider how much people have to read. If you target agents specific to your topic who have sold similar books, however, and you have a damn good proposal, you should see interest soon. That last part is obviously the hardest.
If you do decide to self-publish, just be certain to check yourself and make sure you aren't rushing through anything. Self-publishing well takes a lot of time and effort. I've seen numerous cases of people deciding they want to just get their work out there and the product is far from ready.
If you have a good platform and many people ready to buy your book, self-publishing might be a great choice, but an agent/publisher will also be impressed by such a platform. Also keep in mind that a publisher will be able to reach more readers by default. If your topic is niche (I'm not sure this is) self-publishing is a better option, but if you can reach a wider audience a publisher will get your book into more hands.
Lots to consider of course, but the most important thing is just to not be too impatient. Be aware that publishing in any form requires a lot of time and effort. The best thing you can do now is a lot of research. Learn as much as you can about both publishing and self-publishing. Find out how to do it right in both cases, what the industry is like, and how it works. There is a lot of great information here, and Research Guy has a good book on the topic as well.
