No you can’t put a Nike logo on a shirt for personal use. This is a copyright and trademark infringement which is 100% illegal. You must have permission from Nike to use their logo.
Many people try to get away with using trademarked or copyrighted images and logos to sell, and it isn’t impossible because we see it all the time. But if you do, you run the high risk of getting caught which in some cases can lead to criminal charges. While it is true that many logos aren’t protected by copyrights they are protected by trademarks. Some people use the terms “trademark” and “copyright” interchangeably, but this is erroneous. Copyrights are generally used for written work, plays and other artistic works while trademarks are used for names, phrases (like taglines) and logos. It is important to note that copyrighted works become public domain 70 years after the death of the original creator or 120 years after the date of first publication. Trademarks can be held by companies indefinitely.
If you wanted to parody an existing logo, you can get away with that, but you would need to alter the Nike logo in such a way that it is a crystal clear parody or satire and not just a slightly altered logo. In the instance of parody or satire, this is not typical of a personal use shirt but rather small companies producing a small line of merchandise they intend to sell on a limited scale. Even in these cases, we hear of instances of big brands fighting this in court. Big brands have deep pockets and top notch lawyers making them victors more often than not in such cases.
All in all, it is better to just buy licensed merchandise from an authorized retailer, especially if it’s just for your personal use.