Your teacher did the right thing teaching the pentatonic first. 5 notes is enough to learn to start with. But if you're finding it restrictive, now is the time to add in more notes.
Knowing what notes are what on the fretboard will be of some use and is not that difficult, so you should glance over it and have the ability to do it if you have to. On the A string, for example, we have A A# B C C# D D# E F F# G G# and back to A on the 12 fret.
but knowing which note is which within the pentatonic scale shape will be far more useful, and should become second nature. The pentatonic major scale consists of I II III V VI I (without IV or VII) which in C is C D E G A C (without F or B.) This is of course the pentatonic scale that you play when you are allowed to play all the notes on the 5th fret. The root note in that position (in this case C) is on the 3rd string.
Draw out (or print from the internet) three copies of a pentatonic scale shape. This can be whatever position you are most comfortable with, but I suspect it will be the ones where you have a certain fret in which you can play all the notes.
Take that C major pentatonic scale and pencil in all the B's and F's. You now have a C major diatonic scale, the full 7 white notes on the piano.
Now, take your second copy of the same position, and pencil in all the B's and F#'s. This is the G major diatonic scale. (Made by adding two notes to the C major pentatonic! Weird, but clever.)
Finally, take the third copy, and pencil in all the Bb's and F's. This is the F major diatonic scale. (From the C major pentatonic. Again, weird but clever.)
These new scales will give you more flexibility, especially in playing single semitone intervals. Include these in your solos bit by bit, starting as trills, and your ear will confirm if you have the theory right.
Now, why did I make you do 3 copies?
Well, take your C diatonic major scale (which is of course the same notes as A diatonic minor, it just depends, which you consider to be the root.)
You now have two ways to think about turning it into an F diatonic major scale. You can either move the whole shape up 5 frets/ down 7 frets OR you can stay at the same place on the neck and turn all the B's into B flats.
You also have two ways to thing about turning it into G diatonic major scale. You can either move the whole shape down 5 frets / up 7 frets OR you can turn all the F's into F sharps.
Of course, with the second method the root note will change to a different string, but it's useful to appreciate the patterns in the notes.
And that's the diatonic. If you get bored with that, you can start adding in accidentals. These are often associated with different styles. For blues there is the blue note, Eb if you are in the scale of C major / A minor. G# and F# are other extra notes you may want to add in. You can find these theoretically with pen and paper, but you can also find them on the fretboard by ear.
But in order to orient yourself with these new notes, it helps to know which note you of the pentatonic you are playing. It will be more useful to say to yourself "that's the third, I need to go outside the pentatonic to play the fourth" than to say:
I'm in C major pentatonic, I know where E is, I want to play an F
I'm in Db major pentatonic, I know where F is, I want to play a Gb
I'm in D major pentatonic, I know where F# is, I want to play a G
etc, through all the 12 possibilities.
Because all 12 of these possibilities are equivalent to the previous statement.
EDIT: Now the OP has confirmed he was asking about scales, I'll throw in this handy diagram of some of the "pencilled in" scales.
It shows two positions of the pentatonic scale (marking the fret on which all notes can be played which would be 5th fret if you are in C major.) The additional notes F and B required for C major diatonic are shown in red.
Where you see red-black on consecutive frets on the same string, that's B-C (generalises to VII-I.)
Where you see black-red on consecutive frets on the same string, that's E-F (generalises to III-IV.)
For ease of understanding it is assumed you will play each of the following options separately:
(1) Use 5th fret and below (cover up the right hand side of the diagram)
(2) Use 5th fret and above (cover up the left side.)
If you do this you will need one F on the 1st fret for (1) and one B on the 9th fret for (2). However you will probably find it easier to play if you substitute for the equivalent notes on the 6th and 4th frets.
By applying the flattening and sharpening of individual notes mentioned above, together with moving scales up and down, in all possible permutations, it is actually possible to define all positions of the diatonic scale just with this diagram.
Disclaimer for any pedants out there: the notes are from the key of C major. It's only correct to call it the scale of C major if you play the scale from C to C.