Is there a limit for how many beacons can be connected to my phone?

Yes. The number of concurrent connections supported by your mobile device will be determined by the BLE chipset and the Bluetooth Stack of your mobile device. In terms of packet collisions, I would not be worried, as a Bluetooth Low Energy Central schedules its connections, i.e. it will communicate with one peripheral at the time sequentially. See Connection timing as a Central.
The nRF52832 and the S132 v6.0.0 SoftDevice supports up-to 20 concurrent connections.