Specific to your own handwriting, no one here can judge objectively w/o
seeing it first. How about scanning a sample and putting it in the
a.c.p-p.binary NG?

My handwriting is not bad; it is not
like that rounded and separated letters some (most) people use though.

Well, proper rounding and separation are core requirements for
legibility, aren't they? The worse these attributes, the more has to be
assumed from context, and context can provide guidance to a reader only
up to a certain point. I can recall an old postwar Pelikan ad that
contained a writing sample that was absolutely atrocious and illegible
(should've gotten the student held back in first grade), and I can read
and write in German!

My gut feeling is that there is a real problem and that the only unknown
is the degree of seriousness.