One of the reasons to have a living trust prepared by an attorney, is that the attorney will know you, have notes in his or her file as to your specific wishes and concerns, and he or she will have a copy of the trust in the file. The attorney then becomes a potential witness in court to authenticate the correct trust. Clients may also have the attorney keep the original of the trust in his or her custody if there is a concern about someone in the family tampering with the original trust.
Having said that, since you did a self-prepared trust; I suggest that you give the original trust document and other estate planning documents to the successor trustee to keep in his or her custody. It is not by mistake that trusts are called "trusts". If you trust your successor trustee to settle your affairs and estate without court supervision, then you should be able to trust them to hold on to your original trust document. Also, upon both of your deaths, the successor trustee would have the original trust to carry out its instructions.
When you decide to amend the trust in the future, that would be an ideal time to consider retaining an estate planning attorney to handle the amendment, and then open a file with copies of all of the relevant documents.
Finally, if there is someone you specifically fear that would attempt to alter your estate plan, you should take steps to make sure that they do not have access to any copies of the trust in order to create new pages altering your estate plan.
The real question is how do you prevent someone from altering your trust document. I agree with the earlier suggestions made to you, and would add that you may want to initial each page. Also, dont be afraid to scan it and save a copy in a safe place and distribute copies to persons you trust.