You’d have to do the research about what schools don’t require LORs. I can’t help you with that.
However, IMO you would really be limiting yourself by only applying to colleges that don’t require teacher recommendations. Think back to what classes you have done well in, have participated in etc. and ask one of those teachers if he/she would be willing to write you a positive letter of recommendation for college. I expect you will be surprised by the response. HS teachers are used to writing LORs and are generally focus on your performance in the classroom so if you were prepared, did well etc. then you should be able to get at a positive letter (even if it may be a bit generic). My S was very quiet in HS and both teachers he asked provided recommendations that were good enough to get him into his top choice college.