By 21118, I would expect manufacturing technology to be so advanced that they could fake any physical evidence you could provide. Instead, I suggest you first convince us, in 2018, using tree rings and isotope evidence. You will become so famous that you are mentioned in millions of different books and records - so many, that in 21118 they will be actively waiting for you.
Combine Tree Rings, Carbon-Dating and Radioactive Isotopes
In your own time, cut down a tree. If you can get one that's more than about 73 years old, that's ideal (see below). Oak is apparently best (assuming you're in Europe). Cut out a section of trunk (i.e. a complete "wheel"), as thick as you can possibly fit in the time machine. Scientists will analyse the hell out of this, and will probably destroy a lot of material in the process.
When you get to 2018, visit a university with a strong archaeology or mediaeval history department. Ask them, acting all innocent, if they could possibly help you work out how old this tree was. When they compare the rings against their records, they will realise, with high confidence, that the tree must have lived in the 14th Century. But you could just have carefully cleaned an antique stump. The real proof comes by taking samples and analysing the isotopes.
Carbon dating shows how long ago something died - because your tree took a short cut, they will see that it only died recently. But a sufficiently resourced fraudster could have grown the tree in a giant warehouse, with artificial lighting and heating to mimic old weather patterns. This would recreate the historic ring pattern in a recent tree.
Your clincher is the low levels of radioactive elements that were created in nuclear weapons explosions. These have contaminated (at low but detectable levels) the whole world since the 50s and 60s, and they would be extremely expensive to filter out of the hypothetical fake tree nursery. If your tree is old enough, a sceptic would have to explain why you paid for expensive isotopic filtering before you could have known about nuclear weapons.
Now you can tell your real story, and they have a high chance of believing you.
Your Own Body
Your own body will feature the same low radioisotope levels as the tree stump. However, as soon as you start breathing, drinking and eating in the modern world, you will start to collect modern contamination levels. If you can immediately find a surgeon willing to sample and analyse your tissues, especially teeth, this will be good evidence. But I doubt many doctors are both ethically flexible and trustworthy enough for this to succeed.
Now that 2018 believes you, it's time to become famous. Accept every offer of academic conferences talks, co-authored history books and talk show appearances. Write your memoirs - if you can't write, make a deal with a publisher to hire you a secretary. If your English is too archaic for the mass market, work closely with a ghost writer. Money is no object - a book written by a genuine authenticated time traveller will sell millions.
Have yourself 3D scanned, and get accurate statues made in granite and stainless steel. Spread copies all over the world - in public museums and protected vaults. Have big chunks of your DNA inscribed on vellum, and your fingerprints etched into titanium and launched into geostationary orbit.
When it's time to leave, launch your time machine as a publicised event in front of a huge live audience. Have it recorded in every fashion - HD video, analogue film, monitoring by every scientific instrument available. Remove all doubt.
Most importantly, every single time, state the date and place of your arrival in the future, as precisely as your time machine can manage. The aim is to get yourself mentioned so many times that unless civilisation collapses completely, some record of you reaches 21118 independently of yourself. Ideally, they are waiting to meet you.
This works even if people in the future don't believe the old accounts. People will turn up at the time and place as an excuse for a party, expecting to have a great laugh at the expense of primitive 2018 people who actually believed in time travel! The very fact of materialising in front of their eyes and cameras will be all the proof you need.*
If They Are Not Waiting...
...you will need additional evidence. Back in 2018, you need to have written a long message, and encrypted it. The encryption key must be very long, to prevent brute-force searches (remember, they have ~20000 years to crack it, with much better algorithms and hardware than we have today). The text must be even longer (otherwise a fraudster could choose a fake decryption key to create any plausible message).
Perhaps it's the uncensored version of your memoirs. Perhaps it's an epic poem you write for a loved one you left in the past. When you encrypt it, do so repeatedly, with every algorithm your colleagues can track down, especially those that are thought to be quantum-safe. You don't care about public key, or "proper" digital signatures (you don't care about repudiation). Remember, it doesn't matter if it takes months of processing time to encrypt the message - you can spend as long as you like in the 21st Century before venturing on. Store your message in as many physical libraries, digital archives, vaults and satellites as you can. The people of 21118 must be convinced that you cannot possibly have corrupted so many copies in recent times, even with their technology. Hopefully, when you arrive carrying the decryption key, the idea that you are a time-traveller is more likely than your being a fraudster.
*Maybe you worry that the "welcoming" committee will immediately gun you down and steal the time machine. No need to panic - you know you will survive to have at least one child in the future. Just don't donate to any sperm or egg banks...