Hi Elijah - what are you thinking you want to do after your undergraduate degree? The reason I ask is that biomechanics could be studied from the viewpoint of biomedical engineering where you're interested in medical devices, or from biology, where you're studying tissue growth, etc. Either way, biomechanics can be pursued at the undergraduate level, so if you are more interested in applying science to solve problems, choose engineering, if you are more interested in the answers to "why" types of questions, pick biology.
I had to look up tissue engineering -- the NIH says it evolved from biomaterials. https://www.nibib.nih.gov/science-education/science-topics/tissue-engineering-and-regenerative-medicine. While the field of bioengineering is rapidly evolving, tissue engineering strikes me a more of a biology-based discipline than an engineering one. And more likely a graduate-level specialty. A few more searches and now I know that tissue engineering is a graduate level subject taught in engineering schools thru their biomedical graduate departments. Interestingly enough, many faculty members have their MD.
https://learn.org/articles/What_is_Tissue_Engineering.html suggests coursework in <span style="background-color: rgb(239, 234, 228); color: rgb(0, 0, 0);">medicine, chemistry, biology, mechanical engineering and material engineering. A well-round biomed or bioengineering program will include that type of coursework in its degree requirements.</span>
Definitely research engineering schools, even those that offer biomedical engineering, to make sure they are offering coursework that pertains to your eventual goal. Check the biology departments at those schools to see what research and coursework is being taught. You can easily access suggested course sequences and course descriptions on-line.
Hope you found the above helpful.