Microsoft Word has a lot of great templates that you can use for a resume and cover letter. I struggle with self-promotion, self-esteem, self-confidence, etc, as well. I think it might help if you look at it as just listing facts, with nothing personal added.

On your resume, you're not going to say "I'm good at x, y, z", you'll have sections where you can present facts.

The first section is usually just your objective, which is literally one sentence saying "I would like a job in ________ to help me gain knowledge and experience in the _______ field."
Then you'll have a section on education where you'll say the school's name, what your major/degree is, when it was (or will be) awarded, and any applicable certifications, or licensures, etc. Only list the most recent and relevant colleges, etc, and make sure that it is the highest degree you have. So if you have a master's, you'll list that information, and not your Bachelor's information.
Then a section for your work experience (if you have any), you'll say the name of the place, where it is, your job title, when you work(ed) there, and then provide a brief description of the job duties in a list format. And do that for your three most recent/relevant jobs.
Then you can add a section for volunteer experience, and list it the same way as you did the work experience.
And then at the end, you can add a section for "special skills" or similar, and that's where you can say things that you're good at. But if saying things that you're good at is problematic for you, you can think of it instead as saying things that you have experience with. For example, you can put down that you are proficient with, comfortable with, etc a variety of skills, including computer skills (such as various operating systems, Microsoft Office, etc), languages you can speak/read/write (specify), etc.

I'm not sure how to help you with your cover letter though, unless you just find a template and fill in the blanks, because a cover letter is very much about promoting yourself. But I hope that I helped a little with the resume part of it!

Good luck!