You could try to perform the inference on your second GPU and see, if if has enough memory:
device = 'cuda:1' # assuming your GTX1030 is cuda:1
model = model.to(device)
with torch.no_grad():
    for data, target in val_loader:
        data = data.to(device)
        target = target.to(device)
        output = model(data)
        ...

If you want to run the prediction simultaneously while training, you could save the current model checkpoints, load them in the prediction script and run the inference part.