top-down-shooter | 2D Multi-platform Multiplayer Top Down Shooter | Game Engine library

I'm currently working on a Top-Down-Shooter and having some issues with collision. My world is made of tiles (64x64). The tiles and the entities are rectangles. The player moves with a speed of e.g 2.74 (and not in pixels for smoother movement). But when it comes to the collision between the player (an entity) and a wall i have some issues. To check if there is a collision i take the current position of my player and his movement speed to calculate where his next position would be and if there is any collision. But i check every pixel on the way, so i cant skip an obstacle even if the movement speed is very high. Let's just say the players current position is X:200 Y:200 and he moves 2.74 Pixels a tick in the x direction. My game now checks if there is any collision at X:201 Y:200, X:202 Y:200 or X:202.74 Y:200 and if not moves the player to that position. If I now try to move the player further in the x direction and there is a wall 0.26 Pixels away the player wont move and leave a tiny gap. I tried to calculate the distance between player and wall and add this amount to the players position but for that I need to know which side of the wall the player hits. Also I want the player to be able to move up and down when the wall he hits is in front of him and the other way around.

Here is my collision method (in Java):