Is it normal for your face to feel heavy after Botox? Can it travel to a different place in your face?

This is very unfortunate you have had a bad experience after having your Botox! Depending on the correct placement of the injections it may be that the Botox is the cause of your immediate symptoms as a side effect. Fortunately, the any negative effects should wear off soon. If they don't wear off within two weeks or you are not happy with your results I would definitely contact your provider for further options.  There are many factors that can play in the immediate migration of the drug and correct post injection instructions are critical with regards to sitting up and not massaging the area. 
Best to you and your health!

Yes the heavy feeling is normal and pretty common with Botox and similar products, such as Xeomin and Dysport. It usually only last a few days to weeks. It takes 7-10 day for the products to completely relax or prevent movement.

Botox usually migrates about 1cm around the injection point depending on the dilution.  If you are concerned follow up with your provider.

It can be normal to experience heaviness for a short time after having a neuromodulator or “muscle relaxer” placed.  Sometimes you can avoid that heaviness sensation by placing it in areas that will not cause things like brow ptosis, eyelid ptosis or other unwanted side effects.  It does not sound like you had an excess injected and likely this sensation will subside.  It is hard to answer directly as I do not know where the injector placed the product.  I would visit your provider and see if eyedrops are necessary for possible lid ptosis or if this is just truly a heaviness sensation which can be normal. Please do not hesitate to call your provider.  They would want to see you if there are any concerns. 

at day 3 there is not much if any effect of Botox.  Give it a week to begin to work well.  The Botox is not traveling. Stop obsessing and relax

Thank you for your question mhead04. I am sorry to hear about your
situation. Botox is a purified protein used to address wrinkles associated with
facial expression. Results are seen a few days after the treatment and the pivotal studies demonstrated that the peak effect is seen 14 days after a treatment. Botox spreads about 1 cm from the injection point. Symptoms associated with areas farther than this likely have a different cause. Please follow up with your doctor for specific recommendations. Good luck!