Wall paint bubbling on edge of window from lack of insulation, how to fix?
What are these big blobs 


Moisture has lifted the paint off the wall


  and could it be because of the light rain?


Yes. 


  Should I leave them or fix?


Fix.


  Could it be because the window is pressed on the wall too much?


No. 


  no rubber seal like in the interior side. Could that be it?


Yes.


  Would a rubber seal prevent the moisture?


Any kind of exterior seal or sealant would. E.g. builders silicone, mastic etc. Before sealing it is necessary to remove any dirt and loose paint etc.


  I read I could use a hypodermic needle and stick glue in there to make [bubbled paint] stick, is that true?


No.

Well you could, but it is unlikely to do any good. It is also likely to take longer than removing the loose paint, sanding and repainting.



A well-made window opening has a sill that slopes outwards so that rain doesn't pool against the window. Your window opening may be badly constructed.