Can pwm pulse damage High Side Solid State relay IC ,driving Bulbs as load
Driver IC part number and link to datasheet would be useful.

Bulb link too possibly. Inrush currents can be immense.

You do not say what driver voltage rating is.




Less likely 


There MAY be an inductive component.
This is not obvious, but a reverse diode across and near loads would check that.


More likey.


Inrush currents for cold bulbs can be immense. Unless your figure of 25A is from measurement rather than form a specification it could be higher. Having the two bulbs in parallel MAY cause one to come up to temperature slowly if one hogs the current as they heat differentially. This seems unlikely, but ... . 

An easy check is to add a series resistor that guarantees maximum driver continuous current rating is not exceeded.
1 Ohm in series is very safe.
0.8 Ohm in series should be safe.
0.5 Ohm in series may well be safe.

See below for why ...



Current limiting resistor:

Load effective on current = Power/Von = (12+5)/12 ~ 1.5A.
Effective on resistance = Von^2/P) = 144/17 ~ 8.5 Ohms.

To limit driver to 15A max at turn on with ~ 0 cold resistance
R = V/I = 12/15 = 0.8 Ohms.
This will reduce bulb operating current to ABOUT V/R = 12 / (8.5 + 0.8) ~ 1.3A and power down to VI = 12 x 1.3 = 15.6 (from the original 17.)

I said "about" as the lower current leads to higher bulb resistance leads to lower current leads to ....   .
So maybe a series 0.5 Ohms.
But a series 1 Ohm would be very safe and provide a good starting position.