Can someone please guide me regarding which touch framework (javascript) I should use to make a tablet app? I am new to this area and I am looking for something which allows me to play with my own UI design comfortably.
I went through sencha as I heard its apt for a tablet app environment but I am (sorry, it might sound odd) not able to make out whether I can use my own UI design to make app in sencha. Or any other framework (stable) allows to use custom UI design?
There aren't any major differences between handsets and tablets, except for the screen size. For example, what you would show in a handset in one long scrolling screen, would be shown in a split-screen on a tablet (I am concentrating on the user-experience here).
Split-screen support in still rare in the jscript frameworks, since webkit browsers didn't fully support scrolling only parts of a page (i.e. an iframe or overflow:scroll divs), this support is only now starting to get materialized with iOS5 (Android already had this since 2.2, but it never worked right). There have been other jscript solutions (like iScroll), but being client code they are not always bringing the full "experience" to the client.
The JQuery-Mobile docs have a version under testing, you can try that in a tablet/handset to see the differences.
Regarding your "own UI design", if you mean colors/icons/buttons that's possible on any framework. Where the problems start is when you want to create custom layouts, and each framework provides partial support depending on what exactly you want to achieve.
In general, I'd say Sencha totally separates you from HTML design - you build everything using JSON controls and it has an extensive events/rendering code (of course you can write your own controls), whereas frameworks like JQuery mobile work directly on the HTML (you specify data-* attributes for the details) and renders it almost the same (ok, it does adds wrapping layers, but in general it's still pure HTML).
As always, "it depends" on what you want to achieve and what you are ready to give up... ;-)