It's always nice to have a separate dedicated server for running the Elasticsearch server but as you are using AWS some of the things which you can do to minimize the issues:

Elasticsearch is a stateful application contrast to your node and react app unless you are storing the state there as well which is not a good idea and due to stateless nature of the applications, autoscaling is very useful as you can on-demand based on the CPU, memory or other metrics scale up or down the instances.

But in case of Elasticsearch or other stateful applications, it becomes tricky as when you scale up or down the instance, shards get relocated if they are not reachable within a threshold which can lead to unbalanced Elasticsearech cluster.

Now in order to minimize these issues:

1. Make sure you can storing Elasticsearch indices on the network-attached disk so that there is no data loss when autoscaling brings a new instance and new instance again should use earlier network attaches EBS(where your data is stored).

2. Make sure you don't create a new Elasticsearch process when you scale up or down the instances according to your autoscaling policy and the Elasticsearch process should be fixed and scale up/down with some manual intervention.

3. If you have to scale up the Elasticsearch cluster then make sure you disable shard allocation to avoid the issues mentioned earlier.

These are some known issues which you might face and there could be even more based on your configuration and while writing the answer itself I felt, it so easy to just have a dedicated instance for Elasticsearch to avoid these weird issues.

I would add to other answers following:

• Elasticsearch performs best if it has enough RAM to keep indexes in entirety in RAM. If the Elasticsearch is competing with Node/Application for RAM it will affect it's performance.
• From maintenance/performance perspective you should consider having at least 3-node cluster. Even if that means you have smaller machines. If AWS is upgrading infrastructure and you have 1 machine, when than 0.05% unavailability hits your search is down. If you need to do maintenance on the node or do upgrades having multiple machines will help with availability.
• Depending on your use of Elasticsearch and how often you update/delete items in the indexes, and how fast your indexes will grow, adding more machines/nodes to the cluster will help with growth.

There are probably many more things to consider, but that totally depends on your application, budget, SLAs etc.