I realize there really is a deeper confidence issue and I am already seeking help for that.
Glad to hear it!
At times I am just paralyzed and unable to do things. I am also bothered by the presence of colleagues in my office, afraid they might judge my work (and at the same time going to a hidden place in the library helps a little but is also very annoying and uncomfortable).
What you are describing sounds reminiscent of obsessive-compulsive disorder (OCD). It might be worthwhile to do an evaluation, if you haven't done one yet. Filling out a symptom checklist to take along to the evaluation can be helpful. Here is one from Tourette Canada that my family has found helpful: http://www.gapacademy.ca/files/checklist_ocd.pdf
Not all mental health professionals are trained to evaluate for OCD. The International OCD Foundation can help you find someone with the right training. Try the "Find Help" section of their website; you can phone them if you get stuck.
As the Tourette Canada factsheet about OCD says:
Possible treatments include behavior therapy like cognitive behavioral therapy (CBT) and exposure and response prevention (ERP), and medication.
For a description of my experience coaching my son in ERP therapy, you may be interested to read this answer. It's just a small example intended to provide encouragement.
And now for something completely different:
It is sometimes surprising what type of activity can boost a particular person's self-confidence, in a general way. It's just a matter of trying things out to see what works for you. Here is some brainstorming of possibilities:
The sky's the limit, really.
And finally, the academic side of your question:
Some projects are more cutting edge than others. You and your advisor may want to think about whether this particular project provides the right level of objective confidence that it will give you a PhD within some reasonable number of years. It is allowed to postpone a particular project if it feels a little too risky for the particular juncture you are at in your life.
I'll give you an analogy. If a medical student knows he is bipolar, and knows that being short on sleep tends to trigger a manic phase, he might decide to choose some other medical specialty than, say, emergency medicine, where he may be expected to work at a 24 hours on, 24 hours off rhythm.
As requested in a comment, some quotes from the above references:
Obsessions are unwanted thoughts that happen over and over again
causing a lot of stress or anxiety and ultimately resulting in attempts to
either ignore the thoughts or to make them go away (fact sheet).
I must stress that the checklist is not designed to be used for self-diagnosis. It's a tool that can be helpful in an evaluation process.
Having watched my son go through the evaluation process, and from reading about OCD, I learned that one of the things evaluators are looking at is the degree to which the person feels impaired. For example, a good writer edits and polishes his writing. But if one is getting stuck often, for long periods -- then the perfectionism might be an impairment, rather than just being an asset.