Is there any band (bracelet) adjustment? or do you have to go to a watch shop to have links removed?

It is a job for your local jeweler as it requires a 'pin pusher' tool.

Watch Bracelet Link Removal Tool - Stauer

https://www.stauer.com > pdfs > manuals
PDF
How to adjust watch bracelet links: Step 1. Flip the watch band over and check the underside. Links that can be removed will have an arrow etched on them.


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1. Use the steps below to remove your band. You must separate the Link Bracelet into two pieces before removing the band from your Apple Watch. While removing the band, don't force the band or twist it. Use the steps below to avoid damaging the band or clasp.Jun 19, 2015

   Remove the Link Bracelet on your Apple Watch - Apple ...

   https://support.apple.com/en-us/HT204831 Apple Inc.
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How to resize or remove links from your Magnetic Bracelet ...

Select a clean, flat work surface where you can perform your watch band adjustment. Put down a piece of felt to protect the face of your Casio. Turn on a lamp near your workspace to better illuminate the watch components with which you will be working.

Lay your Casio face down on the protective felt. Look for the small arrows on the back of some of the watch links; these arrows indicate the removable watch links and the direction their pins should be removed.

Locate the pin hole above the arrow on the removable watch links. Insert the tip of a watch pin removal tool, or push pin, into the pin hole. Apply pressure to the link pin, in the direction indicated by the arrow, to free the pin and remove the link. A pair of needle-nose watch or jewelry pliers can be used to help pull out stubborn link pins. Remove as many links as necessary for your watch to fit perfectly.

Reserve the links and link pins that you remove from your Casio Edifice watch. Store the removed watch components in a small, clear, plastic zipper bag. These components can be used when repairing or expanding your Casio watch band.

WARNING:Casio recommends that customers have their watch bands sized by an authorized Casio watch dealer. Sizing the band of your Casio Edifice yourself may void the manufacturer's warranty on your watch. Contact Casio customer support for more warranty information.

Self-adjusting bands usually feature easy to remove links that simply snap out. They usually look just like the main clasp or blend in with the band. Simply locate these links and undo the closures to remove or add them.

Making the Band Shorter
1. Step 1 Stand the bracelet up on its side. Look for arrows on the inside of the bracelet.
   
2. Step 2 Insert a small pointed tool from your hobby or watch set into the tiny holes on the edge of the bracelet. Insert the tool in the hole at the base of the arrow. You will see two holes on the edge of the band. Both pins need to be removed.
   
3. Step 3 Push the pin out with force in the direction the arrow is pointing. Repeat this process on the second pin. When the pins are removed the link will be loose.
   
4. Step 4 Remove the link from its neighbor and replace one pin to secure the bracelet.
   
Making the Band Longer
5. Step 1 Remove the link closest to the clasp by putting a small, pointed tool into the tiny hole on the edge of the watch band.
   
6. Step 2 Push the pin out so the link is detached from the clasp.
   
7. Step 3 Put a new link next to the detached link and line them up so a new pin can go through their holes and attach them together. You may need to snap them together depending on the type of Citizen bracelet you have.
   
8. Step 4 Place the pin into the hole on the edge of the band and push the pin through the band with your sharp tool to attach the two links.
   
9. Step 5 Repeat this process if you need to attach more than one link.
   

mcdevito75 here, Many watches built today are not comming out with replacement Bands (straps, Bracelets) from the factory, the cost of makeing and keeping extra bands on hand is too high, they should at least have a few extra links to replace worn ones. Chances are your warantee is over on the watch and in that case, you"ll have to find another band, Bracelet on your own. Best Bet, visit a small watch repair shop in your area for another bracelet, band, Strap.

Unscrew bracelet screws from the side and take out/add link. Then screw bracelet screws back.

On most brands, there are pins that form hinges for the links of strap. You need to push them out to remove links. Usually you would find arrows marked from inside of the metal bracelet which show you the direction in which to remove the pins. You can remove it if you have a small watch maker's screwdriver but you have to be careful. or get one of these ..
http://www.amazon.co.uk/Watch-bracelet-link-adjuster-remover/dp/B001ZKIL2S/ref=sr_1_1?ie=UTF8&s=watch&qid=1254695541&sr=8-1

which should help you to remove the link pins safely without scratching.

The links most likely need a tool that will push the pins out so you can adjust the bracelet. This can be easily done by any jeweler or watch store. You can also order these types of tools online to do it yourself at home. Please do not attempt to remove links without the proper tools as you will not be able to remove them and you will also damage both the bracelet and the pins.

The segments of your bracelet are held together with friction pins which have to be removed first in order to adjust it. This is a relatively complicated task requiring experience and a special tool to remove and return the pins and bushings back correctly without compromising the bracelet strength.
I recommend taking your watch to an Omega authorised dealer for adjustment while you wait.