I would not worry about the speech limitations at all. You cannot help the condition you are in but you can continue to practice various pronounciations of words and phrases to improve your speech. A disability of sorts is not grounds for acceptance or not being accepted. The key is to just work as hard as you can on your prerequisites, volunteer, and have as many activities to show diversity as possible.
On the other question, would I feel angry or bothered with someone like you in my class...Hell no!!!! I understand that all people have various problems, whether mental; physical; or spiritually, and discrimination is no answer to that. Hell, I am a 29 year old Black man that has been counted out from day one. I was considered unintelligent and unable to learn because I was Black and nonsociable. I graduated with a good GPA, and currently I am a consultant, technology, for the largest consulting firm in the world. I am now switching focus to Pharmacy school and will be there next year. My goal is UCSF, Boston, or WSU.
Keep your goal in sight and do not let a speech issue stop you.