Looks pretty good already!
The problem that you're encountering are collision polygons.
Since your game is highly dependent on collisions, it's important that the collision polygon of your player fits exactly between two obstacle blocks and that the shape is the same.
To achieve this, you'll have to look at the size of your player and your obstacles.
If an obstacle is 50 x 50 pixels, your player collision polygon must not be bigger than 48 x 48 pixels.
(If it was 50 x 50 or 49 x 49, it would not fit between two obstacles)
And you will also have to make sure that both the obstacle and player collision polygon's dimensions are 1:1 (=quadratic).
Here is a .capx demonstrating what I mentioned. Note how the player is 48x48 and the tilemap obstacles 50x50.
Hope this helps.