You need to notice that the mouse has been lifted in the MOUSEUP event.
When another MOUSEDOWN occurs, you need a new set of POINTS()
That suggests an array or a dictionary of Points() arrays.
This may be a stretch for you at the moment
You notice the mouse has gone up in MOUSEUP, so you store a 'magic point' which is (for example) -1000,-1000
Then your PAINT event becomes:
Dim i As Integer
If points.Ubound<1 Then Return
For i=0 To points.Ubound-1
if (points(i+1).left = -1000 and points(i+1).right = -1000 ) or (points(i).left = -1000 and points(i).right = -1000 ) then
//dont draw to or from the special point
//just in case out of range