PHR can take 130mA No Problem even 150mA no problem However they will not last long there.
Even at 120mA your looking at ~ 1 year of light use and a couple months if you use it only 1 minute a day.
PHR-803T are best to run at 90mA to a Max of 100ma.
If your diode still feels warm to the beam of your hand its possible has degraded, You not giving it enough battery supply or you dont know what to expect from a ~90mW-100mW 405nm laser and possible do not have anything to compare it too. With a 405-G-1 lens you should be getting If it is running at 130mA ~150mW. It should light a match no problem.
The Second dot most likely is what TJ said is that your diode is damaged But i think its from another factor other then running it at 130mA. Possible to much heat when soldering to the diode.
The second dot can also appear if the diode is NOT pressed in evenly. This will make a reflection IIRC that will cause a second dot.
What driver are you using.?
What batteries or Battery are you using.
How did you set the currant on your driver.? Did you use a testload.?
Pictures of you setup will help.
Your diode possible can still be good. If you want to give it a shot to check it out.