Yes, you can build your own fence just make sure it complies with zoning laws and any neighborhood covenants, conditions and restrictions.
Nothing I say while answering your question is legal advice. My answer does not form an attorney-client relationship. You should hire an experienced attorney to answer your specific legal questions.
You may build on your own property, but first check local zoning and building ordinances and codes to see whether there is a set-off requirement between the fences. You may be required to obtain a permit and there may be height restrictions and restrictions about the materials used, etc. Also, neighborhood associations sometimes have rules about fences, so if you belong to an association you will want to check that also. Also - be sure to call call to confirm the location of local utilities before you dig as you could be injured or liable for injuries caused from severing a power line, propane line, water line, etc.
You can reach Martin D. Koop at (419) 447-2521 or email@example.com. Martin Koop is an attorney licensed to practice in the State of Ohio. Answering your questions does not create an attorney-client relationship between anybody and Martin D. Koop. You should speak with an attorney to whom you have provided all the facts in your case, before you take any actions or make any choices that may impact your legal rights. I am not obligated to answer subsequent emails or phone calls unless you have formally hired me. I wish you the best of luck with your legal matter.