My long term relationship got fvcked off a few months ago when she broke up with me and for weeks I've been feeling great however I keep getting these random strong urges to do things like message her, unblock her on fb etc. I haven't acted on them and really don't see myself doing that because I have too much respect for myself but is this common?
Yes, it's normal. When you date someone long-term, part of your habitual daily routine involves doing something for/with her. Even though she broke it off, you are able to consciously move on from her, but your sub-conscious still has to get adjusted to not doing things for someone that's no longer there.
It's kind of like a baby that's been sucking pacifiers since birth. If their mom gets rid of all the pacifiers in the house, the baby will eventually realize it can't get anymore; however, the habit of putting something in their mouth and sucking on it is still very much a part of them since they did it habitually for years. This is why they usually resort to sucking their thumbs/fingers instead, and it can be YEARS before they finally stop doing it (I had one cousin stop when she was 17, how disturbing is THAT?!?).
So yeah, you'll have days when you want to do something nice for her or talk to her, even though you mentally get that you shouldn't because she dumped you. The important thing is to recognize what these urges are - habits you picked up while dating her vs. actual feelings of desire for her - and not act on them accordingly. Hope this helps!