Has my beard transplant gone wrong? Hair growing perpendicularly?

It was put in that way. You can't fix it.  The direction of hair growth is how your doctor made the incision sites.  You can't fix the direction.   

The direction of growth of hair following transplant is dependent on the proper positioning of the graft in the recipient site, along with the proper design or pattern of placement.  If the recipient sites are not created appropriately, the result will be irregular and unnatural appearing.  With regard to correction options for your concerns, you could possibly have follicular unit extraction and reimplantation.  

The direction the hair grows is a very important part of hair transplantation.  This is determined by the direction the hair is implanted during surgery.  It is one of the many reasons why patients should be very careful about who exactly is doing the hair transplant.  Make sure your surgeon is board certified by the American Board of Plastic Surgery.  It is unlikely to be corrected at 1 year after surgery.  Graft excision will likely lead to scarring.  Laser hair removal may or may not help.  Good Luck