Can I increase the resolution of my low resolution image?

Generally, no.

Once you have scanned an image at too low a resolution, the damage has been done and the information you need in order to do a successful raster to vector conversion has been lost.

Increasing the resolution of the low resolution image won't bring back the details of a shape, or separate two touching entities.

To take an example from another article:

Original drawing   Desired vectors
Original drawing
 
  Desired vectors
 
Suitable for raster to vector conversion   Not suitable for raster to vector conversion
Scanned at good resolution:
Circle looks like a circle

 
  Scanned at too low resolution:
Circle looks like a diamond

 

If you take the too low resolution image and simply double its resolution in a program like Photoshop, you will end up with this:

Not suitable for raster to vector conversion

The circle still looks like a diamond - its shape has not been improved - but now each 'step' in the diamond is made up of four pixels instead of just one.

The only way to increase the resolution of most low resolution images is to re-scan the original drawing using a higher resolution.