Can I combine two Internet connections into one PC using only a switch?

The easiest way to configure this would be to use a Multi-WAN router such as the Linksys RV042.

Technically: yes

In practice, it's an exotic and expensive configuration.

You can put more than one address on an interface or use more than one interface and be multihomed.

However, this is much more likely to be effective for a big server cluster in a data center.

Expensive routers capable of running routing protocols will be needed and then it still would not help you with a single given TCP connection.

If you try this as a single user of two retail ISPs, then you will have two different IP addresses, so incoming traffic will use the one you made the outbound connection on, and it's unlikely that any equipment you have can be configured with more than one gateway.

A large site with a /24 or shorter prefix and their own ASN can actually announce a single IP address over multiple networks, but that won't work without being further upstream than a retail ISP line.