discovering

Today  I went to the library, only to find there is no seat on floor five ,so I had to go to floor six.I then found that I am a bad mood because I do not like strange placse as I prefer familiar places. Consequently I discovered that I am a single-minded girl.

single minded girl means more independent minded rather than some one that sticks to familiarity.

Discovering

Today, (when) I went to the library, only to find there were (is) no seats available on floor 5,so I had to go to (the) floor 6.Then,I found I was in (am) a bad mood because I did (do) not like the strange place and (I) preferred  (like) the familiar place. So, I discovered that I am a single-minded girl.

Your article is written in the past tense. as you start with 'went',  the past tense of the verb 'to go'. So, you need to ensure all the verbs you use reflect the past tense. I have changed some tenses to make it read a little better - for instance, 'found' is past tense and goes with 'was' - also past tense. If you used 'find' then you could use 'I am' as both are present tense. Similarly, you should say 'did not like' - past and not 'do not like' which is present. In the final sentence you used the word 'discovered; - past tense, which was perfectly correct.