How to grow traffic on a blog within a short time period? What are some tools for that?
To firmly say you’ll get X amount of traffic in Y number of days would probably be a false assurance. But in general, yes, you can grow traffic in a relatively short time period, especially if you mean shorter than the speed of most websites. How?

Let’s talk about your issue now. As you said that you want to increase traffic on your blog, in this context, I would like to say that it depends on the niche of the blog and the quality of your writing. I assume that you must be writing very well, so now you have to know how to make your content accessible to the people for the first time. Because once people started visiting your blog, they would come again, to read new blogs, and tell others about it. Traffic draws more traffic. Instead of telling you all the same things to grow traffic, I would like you to once look at my profile where I have written long answers to queries that are similar to yours. If you do not understand anything there, then you can leave me a reply. Still, for now, I would like to name a few ways.
1) By frequently writing blog posts.
2) By using social media to increase the reach of your blog.
3) By using more pictures in support of your writing in the blog.
4) By adopting proper techniques for search engine optimization of your web content.
5) By using paid methods to promote your blog.
But now I will tell you here about the most important method, which will answer the second part of your question. Apart from the ways mentioned above, this method provides you with some more ways that are reliable and promising. Anyways you are looking for a tool too, if you find something more than a tool, it is a good thing.
According to your needs, the method will be perfect at this time, that is One Minute Free Traffic (OMFT). Of all the methods I have tried so far, this seems to me to be the best. It is a roughly one-hour-long video program teaching you how to get free traffic from just a few minutes of work per day. Free methods or tools usually have limited capabilities, that is the reason they are free. To invest money on a method that stays for life and teaches you skills that are promising would be a better decision in my point of view, instead of purchasing a tool that performs limited tasks for a fixed time. If you need traffic (and everyone does) this is simply the best bang for your buck. Because OMFT has done so much for me, I have so much to say in appreciation of it. I hope this helps solve your traffic problem.
Before finishing the answer, I would like to say that whatever method you pick, it should get you the desired results within time. You will have to be patient to some extent, as we always want things to work faster, but doing these things will help your site get traffic faster than most.
Good Luck!
Thanks,
Cleo