*AsuitablemumI am so sorry you had this sad experience and for all the emotions it may have left you with.
I agree with lots of wise posts, that things could go either way etc. But I feel as you may be wise to pursue this now if this is what you want to do.
Please do get some advice from a suitable organisation or counsellor, please do find someone who can support you through this without being over bearing, e.g. an understanding friend.
As a mum to a boy (of 5) who joined us by adoption, I would personally want to know what my child was doing, even if they were an adult. I might feel threatened (I do hope not) and I feel sure I might feel much worse if I found out by accident.
Do your parents know you found out your birth mum had died?
Of course, I can't guarantee your mum or dad (adopted dad) will be OK with it or fine etc but I just think if you can talk calmly before you start the next bit of your search and explain that it is not to do with failing on her part or your dad's part, that you want to trace birth dad etc or wider family, they may be more supportive. But you know them so do trust your judgment.
As ClassicCoast said "After a while I realised it wasn't my burden to carry that as an adoptee I had a right to do it without guilt that I didn't need to be stuck I the middle worrying about other peoples' feelings."
I expect you have heard of this organisation.
[[http://www.afteradoption.org.uk/
Good luck. 